What is the historical basis for the Exodus?

600,000 men with elders, wives and kids have been reasonably estimated to be about two million. A procession such as this which normally aren't more than a few abreast would have stretched for hundreds of miles. At some point someone would be passing through a town or village and couldn't possibly get lost. Also when they crossed the Red Sea, they were still in the Egyptian New Kingdom and would have been picked up, especially after killing an Egyptian army. the story beggars belief.

This would suggest the Biblical description could be correct and the Egyptians then describe a threat from a revolting population. Though we still have the problem of such a sizable population getting lost in the Levant, that is my answer. You are never going to find evidence of something that never happened only logic from the evidence we do have says that it couldn't have.

UCSD held a fascinating conference on the topic of the Exodus a couple of years back, which I highly recommend viewing - It contains a variety of views on the subject, along with both archeological and textual attempts to support the various hypotheses.

That the Exodus story as described in the Old Testament is a myth, is a pretty much universally agreed upon fact. The debates within the archeological community are focused on whether or not the myth is based on some actual historical event, and when and what that event could have been.

There are a couple of major issues with the Biblical story which have formed the consensus on the matter:

• The numbers aren't very realistic, 2 million people would be stretch out for the entirety of Sinai and leave Egypt without half their population, that would have left catastrophic effects on the Egyptian economy.

• The Egyptians ruled Canaan at the time of the purported Exodus according to the Biblical dating, and for hundreds of years later.

• Cities and nations mentioned in the story did not exist at the time, Camels did not arrive to the Levant until ~500 years later.

• The conquest is not supported by the archeological evidence - some of the cities mentioned were abandoned long before, while others show no sign of destruction during that period.

As Richard Friedman cynically put it, "we're living in a great age, in which we have achieved archeological confirmation of the obvious".

So, if the biblical story is mostly unreputable, the question remains as to how this story was created. Academics opinions differ wildly on this topic. While some (e.g. Mazar) believe some ancestors of the ancient Israelites indeed came from Egypt, others such as Finkelstein believe that the Israelites were essentially an offshoot of the local Canaanite population based on the lack of transitions in the material culture. I'd really suggest watching some of the conference as it really highlights the wide range of theories on the origin of the story.

As a complement to other answers, and especially to nbubis' answer.

Based to a large extent on the work of the Israeli archeologist Israel Finkelstein (a youtube video with him talking on this topic HERE; other similar videos are easy to find) the general problem of advancing from "biblical archeology" (archeology that aims at proving that biblical stories are describing historical facts) to archeology as such is rather well presented in the book Oltre la Bibbia. Storia antica di Israele (2003) by Mario Liverani (Israel's History and the History of Israel), which I have read in a French translation, La Bible et l'invention de l'histoire, Bayard 2008, Gallimard. More works by Liverani: here.

Here are a few pages (Part II, chapter 14, section 4, from page 278) that would illustrate the main argument that could explain how the story may have been elaborated, what the history of the text may be.

As for the probability of it being a true fact, the other answer has mentioned decisive proof against it. I would only repeat that Canaan was occupied by Egyptian forces before the possible date of the Exodus until centuries after that. The Exodus would have taken place inside the Egyptian empire, Canaan wouldn't have been a safe place, it wouldn't have been "out of Egypt" anyway, Egyptian garrisons would have met the refugees upon their arrival in Canaan etc. Egyptian ideological and cultural influence, including Egyptian origin of some names, appears normal in this context. The map of the area is that of the Egyptian empire.

I have highlighted some important terms.

(I had initially posted my own translation from French. Thank you @LаngLаngС for the official English version!)

In these eighth-century formulations, the motif of arrival from Egypt was therefore quite well known, but especially as a metaphor of liberation from a foreign power. The basic idea was that Yahweh had delivered Israel from Egyptian power and had given them control – with full autonomy – of the land where they already lived. There was an agreed ‘memory’ of the major political phenomenon that had marked the transition from submission to Egypt in the Late Bronze Age to autonomy in Iron Age I.

We should bear in mind that the terminology of ‘bringing out’ and ‘bringing back’, ‘sending out’ and ‘sending in’, the so-called ‘code of movement’, so evident in Hosea, had already been applied in the Late Bronze Age texts to indicate a shifting of sovereignty, without implying any physical displacement of the people concerned, but only a shift of the political border. Thus, to take one example, the Hittite king Shuppiluliuma describes his conquest of central Syria in the following way:

I also brought the city of Qatna, together with its belongings and possessions, to Hatti… I plundered all of these lands in one year and brought them [literally: ‘I made them enter’] to Hatti (HDT 39-40; cf. ANET, 318).

And here is another example, from an Amarna letter:

All the (rebellious) towns that I have mentioned to my Lord, my Lord knows if they went back! From the day of the departure of the troops of the king my Lord, they have all become hostile (EA 169, from Byblos).

Egyptian texts also describe territorial conquest in terms of the capture of its population, even if in fact the submitted people remain in their place. This is an idiomatic use of the code of movement (go in/go out) to describe a change in political dependence.

But when, towards the end of the eighth century, the Assyrian policy of deportation began (with the physical, migratory displacement of subdued peoples), then the (metaphorical) exodus from Egypt was read in parallel with the (real) movement from Israel of groups of refuges from the north to the kingdom of Judah (Hos. 11.11). The inevitable ambiguity of the metaphor of movement gave way to a ‘going out’ which was unambiguously migratory, though it maintained its moral-political sense of ‘liberation from oppression’. The first appearance of this motif occurs, significantly, in the Northern kingdom under Assyrian domination.

Thus in the seventh century the so-called exodus motif took shape in proto-Deuteronomistic historiography. The expression ‘I (= Yahweh) brought you out from Egypt to let you dwell in this land that I gave to you’ (and similar expressions) became frequent, as if alluding to a well-known concept. Evidently this motif, influenced by the new climate of Assyrian cross-deportations, and the sight of whole populations moving from one territory to another, was now connected to the patriarchal stories of pastoral transhumance between Sinai and the Nile Delta, to stories of forced labour of groups of habiru (‘pr.w) in the building activities of the Ramessides, and to the more recent movements of refugees between Judah and Egypt: such movement was therefore no longer understood as a metaphor, but as an allusion to an actual ‘founding’ event: a real ‘exodus’, literally from Egypt.

Just as in Hosea the Exodus motif already provided a metaphor for the Assyrian threat, so in prophetic texts of the exilic age the exodus became (more consistently) a prefiguration of the return from the Diaspora – at first, fleetingly, from the Assyrian, to a (still independent) Jerusalem; then firmly, from the Babylonian diaspora:

Therefore, the days are surely coming, says Yahweh, when it shall no longer be said, ‘As Yahweh lives who brought the people of Israel up out of the land of Egypt,’ but ‘As Yahweh lives who brought out and led the offspring of the house of Israel out of the land of the north and out of all the lands where he had driven them.’ Then they shall live in their own land’ (Jer. 23.7- 8; 16.14-15).

At the conclusion of the whole process, in the sixth–fifth centuries the entire story of exodus and conquest of Canaan had been re-elaborated in the light of the real events of Babylonian deportation and return of exiles, thus in effect a ‘new exodus’, prefigured by the mythical one.

What I also found very interesting in this book was the argument against the actual historicity of the massacres against Canaanite peoples that the Bible boasts about (herem). There is no place here anymore for more details about that, but to put it shortly: the real peoples of Canaan that existed and continued to exist there were conveniently excepted from that harsh treatment; the ones that were put to sword are imaginary or lived hundreds of years before. (The "motif" is maybe inspired more by Mesopotamian/Assyrian ideology — than by the Egyptian.)

Among the presentations linked in the other answer there is one by I. Finkelstein, but the one by Robert Mullins seems to me even closer to Liverani's book. The map above is from that presentation (6:37).

I'll summarize what the Jewish Study Bible, 2nd edition says about the subject. This material is from the introduction to Exodus and two essays: "The Religion of the Bible" and "Archeology and the Hebrew Bible".

Positive evidence: We know that Semites of similar ethnicity to the Hebrews had for centuries migrated to Egypt in search of food and water during famine; others were brought there as slaves. Some of the Asiatics (as the Egyptians called them) were engaged in royal building projects, like the Hebrews of Exodus. The name "Moses" is of Egyptian origin--the etymology in the Bible is invented. It seems odd that the Israelites would invent a story about being slaves in another land and invaders of the land they inhabited. The numbers are certainly exaggerated--the wilderness could never have supported 600,000 Israelite men plus women and children--but it's not implausible that the exodus has a historical kernel of truth.

Negative evidence: There is no reference to the exodus in Egyptian records, although Egyptian records typically record only victories and not defeats. There is no extrabiblical evidence of the ten plagues or of a massive escape of slaves. All attempts at identifying archeological evidence for the sojourn in Egypt and for the exodus have been unsuccessful. The conquest of Canaan portrayed in Joshua and Judges, where the Israelites utterly destroy the native Canaanites, directly contradicts archeological evidence. Canaanite sites show no evidence of large-scale destruction at the end of the Bronze Age, and early Israelite sites are very similar to older Canaanite sites. Even the Israelite religion was similar to that of the Canaanites--in the oldest poetry of the Bible (like the Song of Deborah and the Blessings of Jacob), Yahweh seems to be a mixture of features attested in Canaanite and Ugaritic religions for the creator god El, the "old god", and the storm god Baal. Even the Jerusalem Temple built by Solomon was a typical Canaanite shrine, with a "holy of holies", an altar, cultic pillars, and elaborate decorations of palmettes, lotus, bulls, and cherubim.