There are few researches on analysis of propagation of elastic waves in solid by the finite element method and in relation to nonlinear response. J. H. Argyris dealt the behavior of a circular solid of elastic perfectly plastic material under an axial impact. Observing actual behavior of ship structures, there are many cases where the effect of strain rate on mechanical properties of material should not be neglected and for dynamic collapse of structures elastic-plastic large deflection analysis is required under impact load. To these problems, a formulation for analysis by the finite element method is made and results of analysis show clearly dynamic effects on the nonlinear behavior of structures.