An explicit, r-adaptive finite element method is described for application to hypervelocity impact and penetration problems. Here, r-adaptivity refers to a numerical scheme in which the nodes of the mesh are moved to improve the quality of the mesh. The r-adaptive scheme implemented here is similar to ALE, in that the physical and mesh velocities are independent; however, in this application the mesh is constrained to follow the physical boundaries of the material. Thus, interfaces do not flow through the mesh. The advantage of this treatment is that the original contact conditions are preserved. The r-adaptive scheme is very effective in controlling the time step in the calculation; however, it is not sufficient to completely control the topology of elements. At that stage an automatic remesh is performed and is confined to a region local to the distorted elements. To illustrate the applicability and robustness of the method, results from low-velocity and hypervelocity Taylor anvil impact simulations are presented. The results for hypervelocity represent the first near-Lagrangian calculations with traditional finite elements ever successfully performed for this application (here, near-Lagrangian implies that the mesh motion is typically everywhere close to the material motion). Strengths and weaknesses of the approach are highlighted. © 2001 Elsevier Science Ltd. All rights reserved.