The study deals with the computer simulation of fluid-particle suspension flow. A mathematical model including the time-dependent Navier-Stokes equations and a modified convection-diffusion equation accounting for shear-induced particle migration effects is applied in the case of highly concentrated suspensions. More detailed results can be achieved treating the particle and the fluid phase separately as two interpenetrating continua which interact through the transfer of momentum. The ill-conditioned systems of non-linear partial differential equations are solved applying the Galerkin finite element method and specially developed splitting algorithms to reduce the large computational costs. The numerical results are pertinent to blood flow as hydrodynamical interactions in the microstructural range play an important role in the rheology of blood.