We explore the perforation process of metallic plates impacted by rigid sharp-nosed projectiles at high velocities. In particular, we are looking at the diameters of the penetration hole in the plates through a series of 2D numerical simulations, in order to check for the occurrence of cavitation in finite-thickness plates. This phenomenon has not been observed by previous workers and we were looking for its effect on the perforation process. Our simulations show that for every projectile/plate pair there is a certain impact velocity which marks the onset of cavitation. These threshold velocities depend on the normalized thickness of the plates, as well as on their effective strength. Our simulations are supported by the results from perforation tests on plates made of a low strength lead-antimony alloy. The main conclusion from our work is that analytical models for plate perforation should take into account the cavitation phenomenon, especially for high velocity impacts.