This paper describes an absorbing boundary condition for finite-difference modeling of elastic wave propagation in two and three dimensions. The boundary condition is particularly effective for obliquely incident waves, typically quite troublesome for absorbing boundaries. Analytical predictions of the boundary reflection coefficients of a few percent or less for angles of incidence up to 89 degrees are verified in example finite-difference applications. The algorithm is appropriate for use in a velocity-stress finite-difference (vs-fd) formulation. It is computationally simpler than a similar absorbing boundary given previously for the standard displacement formulation. A second algorithm is presented which may be advantageous when the boundary of interest is exposed to strong evanescent waves. Both algorithms require that the adjacent elastic medium be locally homogeneous.