One of the purposes of this study is to compare several direct time integration methods in wave propagation problems in solids. Amplitude decay and period elongation are used as the basic parameters in order to compare the integration methods. The specific methods are Central Difference Method and the Newmark's generalized acceleration method. Another purpose is to get some information about the direct time integration method in the step pulse propagation analysis which occurs in blasting and impact of solids. The Newmark method with varying γ-coefficient shows good results in one and two dimensional step pulse propagation analysis.