Appius Claudius Caudex was a patrician member of the Claudii. He was the grandson of Appius Claudius Caecus, and served as consul in 264 BC.

In that year, he drew Rome into conflict with Carthage over possession of Sicily. In 265 BC, Hiero II of Syracuse had attacked Messina in an attempt to recapture it from the Mamertines, mercenaries from Campania who had taken it from him some years before. The Mamertines allied with a nearby Carthaginian fleet and held off the Syracusans, but when the Carthaginians did not leave, the Mamertines appealed to Rome in 264.

Some senators were opposed to helping them, but Appius Claudius persuaded the citizens to support them. He led a force to Messina, and as the Mamertines had convinced the Carthaginians to withdraw he met with only a symbolic resistance. The Mamertines handed the city over to Appius Claudius, but the Carthaginians returned to set up a blockade. The Syracusans, meanwhile, were also stationed outside the city. Claudius tried to send ambassadors to both the Carthaginians and the Syracusans, but he was ignored. He then led his troops outside the city defeated the Syracusans in battle, and Hiero retreated back to Syracuse. The next day Claudius also defeated the Carthaginians.

This dispute was one of the immediate causes of the First Punic War.