AbstractIn this paper, we introduce a structure‐preserving method based on the symplectic discrete singular convolution differentiator (SDSCD) for simulating elastic wave fields. In the method presented for solving elastic wave equations, physical space is discretized by the singular convolution differentiator, whereas a symplectic difference scheme is used for the time discretization. With this method, the computational accuracy and stability have been greatly improved compared with traditional pseudo‐spectral method. Numerical results suggest the SDSCD algorithm can suppress effectively numerical dispersion, and is suitable for modeling the large‐scale and long‐duration seismic wave propagation.