A numerical algorithm is developed to calculate electrophoretic mobilities of rigid model polyions that includes the effect of ion relaxation. The Navier-Stokes, Poisson, and ion transport equations are cast into forms that are amenable to numerical solution by boundary element procedures. The three equations are solved simultaneously by an iterative procedure. It is applied first to a spherical polyion containing a centrosymmetric charge distribution and double layer that is not thin compared to the radius of the sphere. Resulting mobilities compare favorably (to within 10%) with independent theory. The algorithm is then applied to spherical polyions containing noncentrosymmetric charge distributions. Although the present calculations are restricted to spherical polyions, there is no formal difficulty in extending them to nonspherical polyions.