In this paper, we propose a method of analysis for some inverse problems in elastodynamics. The inverse problem under consideration is defined such that the shape and location of an internal defect in a structural component are not known, but the displacements on some part of the boundary are given as additional information. The integral equations are derived in terms of the modification for an assumed defect shape from the well-known integral equations for elastodynamic problems by a Taylor series expansion. The boundary element method is then applied to the numerical implementation of the resulting boundary integral equations. The computer program is developed for two-dimensional problems. The effectiveness of this method is revealed through numerical computation for a couple of sample problems.