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A time-marching Euler calculation for 2-D and quasi-3-D unsteady flows in oscillating blade rows is presented, based on a finite volume scheme with cell-vertex discretization in space and 2-step Runge-Kutta integration in time. Extra fluxes due to the deformation of the moving finite volumes are directly included in the conservation equations in the physical coordinate system. A zonal moving grid technique is used, in which only subregions near oscillating blades are moved to fit both the moving (blade) boundaries and fixed regions. For phase-shifted periodic conditions, the conventional “Direct Store” method is used as a basis for comparison. Two alternative methods to save computer storage are proposed and preliminary demonstrations of their usefulness are given in the present calculations. Calculated results for unsteady flows in an oscillating flat plate cascade are in good agreement with those from two well …