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The scattered field is studied that results when a plane wave is normally incident on a perfectly conducting flat plate in motion. The exact solution is analyzed for both periodic and aperiodic motion. The quasi-stationary approximation is compared with the exact solution, and the error is found to be on the order of where is the maximum speed of the moving boundary and is the speed of light. This error estimate includes a factor which increases as the distance from the plate increases. A uniform quasi-stationary approximation is developed which has an error on the order of independent of the space variable. By taking into account the Doppler shift, it is possible to construct a uniform approximation to the exact solution on the order of where is the maximum acceleration of the boundary.