We have studied the process of nanosecond compression pulse propagation in metal (aluminum, copper, and steel) foils. It was found that the compression pulse velocity in the foil may significantly exceed the longitudinal sound velocity in the corresponding bulk material. The results emphasize the necessity of very carefully interpreting the data for submicrosecond and shorter impact loading. The presence of a sufficiently long nonstationary shock wave process at the surface subjected to a short impact perturbation (with the wave characteristics significantly differing from those of a steady-state wave process) requires a more detailed analysis of the mechanism of shock wave formation in solids taking into account their discrete structures.