Abstract: A numerical method is developed for simulation of rotor-stator interactions in a compressor or turbine stage.This method solves quasi-three-dimensional Navier-Stokes equations by an implicit high resolution finite volume method.A fully conservative method is designed to compute the inviscid and viscous flux at the interface of rotor and stator grids.Numerical results of rotor-stator interactions in a transonic compressor stage at off-design conditions are presented.The mechanism of rotor-stator interactions in this compressor stage is discussed in terms of the computational results.