In the boundary element (BE) solution of wave propagation, infinite absorbing elements are introduced to minimize diffractions from truncated edges of models. This leads to a significant simplification and reduction of computational effort, especially for 3-D problems. The infinite BE absorbing boundary condition has a general form for both 2-D and 3-D problems and for both acoustic and elastic cases. Its implementation is facilitated by the introduction of the corresponding shape functions. Numerical experiments illustrate a nearly perfect absorption of unwanted diffractions. The approach overcomes some of the difficulties encountered in conventional absorbing techniques and takes less memory space and less computing time.