In this work, an off-surface boundary integral (OSBI) method is presented as a mesh termination scheme for solving large or infinite domain problems of elastodynamics. The boundary integral equation is discretized using finite element shape functions and the Neumann boundary condition term is solved for in terms of the Dirichlet boundary condition term. This expression is then substituted into associated finite element formulation for the interior problem. Comparisons are made using the new OSBI technique, the DtN method of Givoli and Keller and several other local nonreflecting boundary conditions. The proposed boundary condition is shown to be accurate, is well suited for use with finite element methods and is competitive with the DtN method. (C) 2000 Elsevier Science S.A. All rights reserved.