Systematic experimental work [S. Zhuang, G. Ravichandran, D. Grady, J. Mech. Phys. Solids 51 (2003) 245–265] on laminated composites subjected to high velocity impact loading exhibits the dispersed wave field and the oscillatory behavior of waves with respect to a mean value. Such a behavior is absent in homogeneous solids. An approximate solution to the plate impact in layered heterogeneous solids has been developed in [X. Chen, N. Chandra, A.M. Rajendran, Int. J. Solids Struct. 41 (2004) 4635–4659]. The influence of the particle velocity on many process characteristics was demonstrated. Based on earlier results [A. Berezovski, J. Engelbrecht, G.A. Maugin, Arch. Appl. Mech. 70 (2000) 694–706], numerical simulations of one-dimensional wave propagation in layered nonlinear heterogeneous materials have been performed. The formulated problem follows a conventional experimental configuration of a plate impact. An extension of the high-resolution finite volume wave-propagation algorithm [R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002] is used. The speed of sound depends nonlinearly on a current stress value in each layer but also on the mismatch properties of layers. Results of numerical simulations capture the experimental data rather well.