A simple, robust numerical algorithm to localize moving boundary points and to interpolate unsteady solution variables across 2-D, arbitrarily overset computational grids is presented. Overset grids are allowed to move in time relative to each other. The intergrid boundary points are localized in terms of three grid points on the donor grid by a directional search algorithm. The parameters of the search algorithm give the interpolation weights at the localized boundary point. The method is independent of numerical solution algorithms and may easily be implemented on any 2-D, single block flow solver to make it a multi-block, zonal solver with arbitrarily overset computational grids. Computational results and comparisons with single grid solutions are presented for flows through a compressor cascade and over an airfoil undergoing a flapping motion. Excellent agreement is obtained against the single grid solutions.