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Methods used to calculate the radiated acoustic field of transient normal surface force sources applied to elastic solids have previously included significant approximations or have constrained the surface force distribution in practically restrictive ways. In this paper, a theoretically exact, quantitative, numerical solution to the problem is described. The only constraint on the applied suface force in this solution is that it is cophased. Nevertheless, by efficient numerical construction, the computational expense required is not inconveniently large. Theoretical results are presented and compared with results in the literature.