The Rayleigh-Benard convection with a superimposed horizontal shear flow in rectangular domains is treated numerically utilizing a finite difference method and experimentally by applying an interferometric measuring technique. The fluid used is silicon oil, a high Prandtl number fluid, Pr = 530. The investigations concern the supercritical Rayleigh number region of 2300 Ra 20 000. The Reynolds number, which characterizes the strength of the throughflow, varies in the range of 3 10 - 5 Re 0.1. According to special parameter combinations of the Rayleigh and the Reynolds number, convective rolls with different orientations can be distinguished. The dynamical behavior of travelling, transverse rolls is also considered.