An overset grid method is applied to the solution of single and multi-passage cascade flows with a compressible Navier-Stokes solver. C-type grids around individual blades are overset onto a Cartesian background grid. Overset grids are allowed to move in time relative to each other as prescribed by the oscillatory plunging motion. The overset grid method uses a simple, robust numerical algorithm to localize moving boundary points and to interpolate solution variables across intergrid boundaries. Computational results and comparisons with single/staggered, deforming grid solutions are presented for in- and out-of-phase multi-passage flows through a compressor cascade. Very good agreement is obtained against the deforming grid solutions.