Analytic and numerical solutions for the problem of the interaction of intense ion beams with matter in the form of plane targets are considered in this paper. The theory of the interaction of protons with matter at low energies is discussed and calculations are presented for the energy loss of protons in aluminum and gold. Zero‐ and one‐dimensional models are developed and the results are compared to numerical simulations carried out with the one‐dimensional Lagrangian hydrodynamic codemedusa[Comp. Phys. Comm.1, 271 (1974)], which has been extended to include the various physical effects needed to carry out realistic simulations of the interaction of ion beams with matter. The theory and simulation of the acceleration of foils by intense ion beams is also considered and representative results are given. The theoretical results are used to investigate the optimum conditions in which to carry out stopping power experiments for ions in hot, dense plasmas, so that the theory can be tested. These results are needed in order to perform more realistic pellet calculations for inertial fusion.