In this paper, we address hydrodynamic interactions of individual red blood cells (erythrocytes) with micro-rough surfaces in a shear flow of a viscous fluid using computer simulations. We study the influence of the microrelief on the dynamics of cell movement. It has been shown that periodic microrelief with typical length scale comparable with the size of an erythrocyte may cause an increase of the repulsive hydrodynamic force directed outwards on the micro-rough wall. The results can be used in the design of microfluidic devices that are intended to operate with whole blood samples.