We develop a new high-order numerical method for continuum simulations of multimaterial phenomena in solids exhibiting elastic–plastic behavior using the diffuse interface numerical approximation. This numerical method extends an earlier single material high-order formulation that uses a tenth-order high-resolution compact finite difference scheme in conjunction with a localized artificial diffusivity (LAD) method for shock and contact discontinuity capturing. The LAD method is extended here to the multimaterial formulation and is shown to perform well for problems involving shock waves, material interfaces and interactions between the two. Accuracy of the proposed approach in terms of formal order (eighth-order) and numerical resolution is demonstrated using a suite of test problems containing smooth solutions. Finally, the Richtmyer–Meshkov (RM) instability between copper and aluminum is simulated in two-dimensional (2D) and a parametric study is performed to assess the effect of initial perturbation amplitude and yield stress.