We present a new hybrid approach to simulate elastic P-SV wave propagation. The method combines a low-order finite-element method (FEM) with a fourth-order velocity-stress staggered-grid finite-difference method (FDM). The FEM is applied to boundaries such as the free surface and fault surface where the FDM has difficulty accounting for the boundary conditions. The FDM is used to propagate waves in the interior regions where the fourth-order staggered-grid FDM is more efficient than the FEM. A minimum of 12 and 6 points per wavelength are used in the regions modeled by the FEM and FDM, respectively. To couple the FDM and FEM, a strong interface, which is 3 or 4 finite-difference grid spacings wide, is constructed between the regions modeled by the FDM and FEM using a newly derived high-order interpolation scheme. The accuracy and efficiency of the interface and the new scheme were tested (1) by simulating a Lamb's problem and (2) by simulating a kinematic propagating rupture on a 45°-dipping fault. Comparisons of results with analytical solutions and those obtained using independent numerical methods show exceptional agreement. We show that in terms of efficiency and memory requirement the hybrid approach is comparable to the fourth-order velocity-stress staggered-grid FDM but greatly expands its applicability by providing an accurate method for dealing with complicated boundary conditions.