A Navier-Stokes solutions method with overset grids is applied to unsteady multipassage 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 multipassage 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 multipassage 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.