I would like to know which kind of siege weapons were used during Punic wars on both sides, there is not very much information around.
There's actually quite a bit available, even just from wikipedia:
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.
As for siege equipment used during the Punic Wars it's quite a long period and should be looked at in a progressive manner.
- When the Roman republic entered the war in 264 BC there was little siege strategy within the Roman army. Their main tactic was the circumvention of an enemy town with a series of palisades and connected fortifications. They would then wait it out, some sieges lasted several months and may or may not have been successful.
- Gradually the Roman army was exposed to Greek culture and technology through their ally Syracuse. They then adopted new machines to their siege train such as the covered ram etc and heavy ballista.
- The Carthaginian army had altogether more advanced Hellenised siege technology at their disposal. Through years of fighting with the Sicilian Greeks they had developed and taken ideas from over two centuries of warfare.