Abstract We show that in relativistic heavy-ion collisions the independent electron model can be used to predict cross sections for multiple inner-shell ionization and capture in a single collision. Charge distributions of 82- to 200-MeV/amu Xe and 105- to 955-MeV/amu U ion beams emerging from thin solid targets were used to obtain single- and multiple-electron stripping and capture cross sections. The probabilities of stripping electrons from the K, L, or M shells were calculated using the semiclassical approximation and Dirac hydrogenic wave functions. For capture, a simplified model for electron capture was used. The data generally agree with theory.