Rotor-stator interaction in turbomachines is considered. A computer program was developed to numerically simulate 2-D unsteady compressible Navier-Stokes equations based on Jameson`s numerical method. In this problem, the sliding mesh method is used at the interface of rotor and stator. The transfer of information at the sliding interface was done based on a conservative form of a third order interpolation technique. Several testes cases were carried out to examine the problem and obtain the effect of rotor-stator interaction. The results show that for the turbine type stages, the stator-rotor interaction affects mainly the moving blades and also the wake region of the stationary blades. The amount of these effects depends on the velocity of the rotor blades.