This paper is mainly concerned with the development of integral equations to compute stress and velocity components in transient elastodynamic analysis by the boundary element method. All expressions required are presented explicitly. The boundary is discretized by linear isoparametric elements whereas linear and constant time interpolation are assumed, respectively, for the displacement and traction components. Time integration is carried out analytically and the resulting expressions are presented. An assessment of the accuracy of the results provided by the present formulation can be seen at the end of the article, where two examples are presented.