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Wave‐propagation effects induced in isotropic materials by either explosive or impact loading uniformly over a planar surface are much simpler than those produced in anisotropic solids in which significant transverse particle motion may occur. Such behavior in linearly elastic anisotropic solids has been investigated previously, and in the present work the analysis has been extended to include elastic‐plastic behavior. A general mathematical description of both elastically and plastically anisotropic materials is presented, and then several specific applications are considered in detail. For the case of an elastically isotropic solid that is plastically anisotropic with a single slip plane and direction, it is found that for certain orientations two plastic waves can be propagated, one of which is quasilongitudinal and the other is quasitransverse. For more general orientations there may be two quasitransverse waves and a single quasilongitudinal disturbance. These results approximate the behavior of a single‐crystal material of hexagonal symmetry, such as beryllium, for which effects of elastic anisotropy are small and slip occurs predominantly on the basal plane. Since there is a single spatial coordinate involved in planar wave propagation, the general equations describing elastic‐plastic wave propagation can be written in one‐dimensional finite‐difference form and solved numerically for arbitrary crystal structure and orientation. A number of specific examples are considered and compared with analytical solutions.