AbstractTwo apparently different time‐domain boundary‐element formulations for plane‐stress/plane‐strain elastodynamic problems exist in the literature. The present paper shows why one of the formulations, which is valid for a particular type of interpolation function, forms part of the other, which can be used with any interpolation function. The main differences presented in the past between the two existing time‐domain boundary‐element methods were based on an incorrect expression of the tractions in the complete plane due to the rectangular impulse load. Results obtained in the past which were presented to evaluate the differences between the two formulations are shown to be incorrect. A compact expression for the fundamental solution integrated along a time step when the time interpolation functions of all the boundary variables are assumed to be piecewise constant is presented. This integral gives the same tractions as those corresponding to a rectangular i