Transparent (or absorbing) boundaries can be used in finite-difference wave simulation to reduce the size of the computational grid and to eliminate reflections from the edges. An efficient and accurate transparent boundary can be formulated by decomposing the elastic waves into dilatational and rotational strains. The wave motions for the strains at the boundary can then be approximated by a one-way wave equation. The direction of propagation is determined at each grid point by the gradient. This transparent boundary condition eliminates artificial reflections for a wave arriving at any angle of incidence and reduces the error to the level of precision of the finite-difference approximation. Application of this transparent boundary condition is restricted to a medium that is homogeneous at the boundary to assure full separation of P waves from S waves. Also, interfering waves that generate phase velocities significantly greater than the assumed group velocity introduce errors. An example of the transparent boundary condition shows that it is a significant improvement over the A1 boundary condition of Clayton and Engquist.