A Navier-Stokes solution method with overset grids is applied to unsteady multi-passage cascade flows, and the unsteady blade loadings are compared against the single passage solutions with the direct store interblade boundary condition. In the overset grid solutions, the multi-passage domain is discretized with O-type grids around each blade and a rectangular background grid. Blade grids are allowed to move in time relative to the background grid as prescribed by the oscillatory plunging motion. The overset grid method uses a simple, robust numerical algorithm to localize moving intergrid boundary points and to interpolate solution variables across grids. Computational results are presented for two and four passage, subsonic and transonic flows through a turbine and a compressor cascade. The overset grid solutions over the multi-passage periodic domains agree well with the single passage solutions and the experimental data. It is concluded that the time linearization error introduced by the direct store approach is negligible in the range of flow conditions studied.