The Carthaginians relied heavily on mercenaries, which later got them in trouble at the end of the 1st Punic War when the Carthaginian senate refused to pay them. Anyway, not much seems to have been written on formations used by Carthage - save Hannibal Barca who frequently changed formation for each situation.

Generally, they do seem to have used Hellenistic tactics and even hired a Greek mercenary general (Xanthippos) for a time in the 1st war. If anything is regular it is elephants in the front and cavalry on the wings.