The modeling with discrete methods of elastic media of infinite extent that are subjected to dynamic loads normally calls for the use of special transmitting (or nonreflecting) boundaries. One such discrete method is the thin layer method, which allows efficient computation of the Green's functions for layered soils of finite depth; its application to elastic half-spaces, however, requires that the infinite medium be represented by means of approximations that are analogous to transmitting boundaries. In this article, we explore the accuracy of two of these approximations in the context of the Green's functions for antiplane (or SH) line loads. We find that the paraxial approximation of Engquist - Majda gives good results, provided that a “buffer layer” with the same material properties as the half-space separates the computational domain from the transmitting boundary. While these results were studied from the point of view of the thin layer method, they apply equally well to models with finite elements or finite differences.