Upvote:4
As for siege equipment used during the Punic Wars it's quite a long period and should be looked at in a progressive manner.
If you need more information try reading JF Lazenby's book on the First Punic War, and Osprey publication Ancient Siege Warfare. (Both sources informed this answer).
Upvote:10
There's actually quite a bit available, even just from wikipedia:
Catapults: http://en.wikipedia.org/wiki/Battle_of_Carthage_%28c._149_BC%29
Trireme Rams, Corvus (naval): http://www.historyofwar.org/articles/weapons_corvus.html
Sambuca, Claw of Archimedes, Heat Ray, onagers (naval): http://en.wikipedia.org/wiki/Siege_of_Syracuse_%28214%E2%80%93212_BC%29#Siege
Battering rams, ramps, roman tortoise, and towers were also very commonly used siege weapons in this time period. If you're writing a paper or article you might research those more thoroughly; I don't know offhand to what degree these were used in the various battles of the three Punic wars.
You should definitely read up on Archimedes, he's credited as being one of the most famous engineers in history, and was active in crafting defenses for his city during the Roman invasion.
You should also review the use of elephants in this war; while not traditionally "siege engines", they were sometimes used to help break through defenses and were a staple unit for Carthage.