The geometry of a conventional two-bladed Savonius rotor was used in this study based on a report available in the literature. A two-dimensional rotor model consisting of two buckets and an overlap ratio of 0.1 was prepared. The unsteady Reynolds averaged Navier-Stokes (URANS) equations and the eddy-viscosity turbulence model SST k-ω were employed in order to solve the fluid motion equations numerically. Instantaneous velocities and pressures were calculated at defined points around the rotor and then averaged. The research shows that the operating rotor significantly modifies the flow on the downwind part of the rotor and in the wake, but the impact of the tip speed ratio on the average velocity distribution is small. This parameter has a much greater influence on the characteristics of the aerodynamic moment and the distribution of static pressure in the wake. In the upwind part of the rotor, the average velocity parallel to the direction of undisturbed flow is 29% lower than in the downwind part.