AbstractA variationally coupled finite element–boundary element method is developed for transient problems. A single variational statement is obtained for the entire domain and the unknown tractions, which may be discontinuous on the interface and are often a source of difficulties, are eliminated. Moreover, no interface conditions need be taken into consideration at the level of the discretized equation. The discrete equations for the coupled system can be obtained directly without any intermediate steps. The method generalizes a coupling method previously developed by the authors for statics. Numerical examples show that the solutions obtained by the present method agree very well with those obtained by analytical solution