Flows around a flat plate during a pitching motion in a uniform crossflow are studied numerically. The flat plate makes a cycle of pitching motion about its mid-chord position at a constant angular velocity. The body-fitted grid generation with moving boundaries is used to obtain the numerical solution of the incompressible Navier-Stokes equations. The time-dependent curvilinear coordinate system which coincides with a contour of a moving boundary is transformed into a fixed rectangular coordinate system in a calculational plane. The changes in the streamlines, C_D and C_L, during the pitching motion are obtained. The results of present analysis show good agreement with those of previous experiments.