This paper is concerned with the development of a general framework for adaptive mesh refinement and coarsening in three-dimensional finite-deformation dynamic-plasticity problems. Mesh adaption is driven by a posteriori global error bounds derived on the basis of a variational formulation of the incremental problem. The particular mesh-refinement strategy adopted is based on Rivara's longest-edge propagation path (LEPP) bisection algorithm. Our strategy for mesh coarsening, or unrefinement, is based on the elimination of elements by edge-collapse. The convergence characteristics of the method in the presence of strong elastic singularities are tested numerically. An application to the three-dimensional simulation of adiabatic shear bands in dynamically loaded tantalum is also presented which demonstrates the robustness and versatility of the method. Copyright (C) 2001 John Wiley Sons, Ltd.