The analysis technique for the problems concerning transient sounds radiated by impacted bodies is investigated based on the boundary element method(BEM) and a general purpose analysis program, which is available for any sound sources, is developed. The Laplace transformation of Helmholtz equation is employed in the formulation of BEM. In Laplace range, the analysis is carried out with the boundary input values converted by numerical Laplace transform. The results in the time domain are obtained by numerical inverse Laplace transform. As a transient sound radiated by impacted bodies, transient acoustic radiation from a sphere and a beam of circular cross section impacted by a sphere are considered. The validity of these analytical results for time dependnt sound radiation is examined by comparing with the experimental results.