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A finite-difference method with spatially non-uniform grids was developed to simulate elastic wave propagation in heterogeneous anisotropic media. The method is very simple and requires less compution time. Complicated geometric structures, such as low-velocity layers, cased boreholes and nonplanar interfaces, are treated with fine non-uniform grids. Unlike the multi-grid scheme, this method does not require interpolation between the fine and coarse grids and all grids are computed in the same spatial iteration. Planar or non planar surfaces including underground lens and cased boreholes are easily treated in a way similar to regular grid points. The Higdon's absorbing boundary condition was used to eliminate boundary reflections. Numerical simulations show that the method has satisfactory stability and accuracy. The proposed scheme more efficiently simulates wave propagation in heterogeneous anisotropic media than conventional methods using regular rectangular grids of equal accuracy.