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SUMMARY In this paper, we introduce the so-called symplectic discrete singular convolution differentiator (SDSCD) method for structure-preserving modelling of elastic waves. In the method presented, physical space is discretized by the DSCD, whereas an explicit third-order symplectic scheme is used for the time discretization. This approach uses optimization and truncation to form a localized operator. This preserves the fine structure of the wavefield in complex media and avoids non-causal interaction when parameter discontinuities are present in the medium. Theoretically, the approach presented is a structure-preserving algorithm. Also, some numerical experiments are shown in this paper. Elastic wavefield modelling experiments on a laterally heterogeneous medium with high parameter contrasts demonstrate the superior performance of the SDSCD for suppression of numerical dispersion. Long-term computational experiments exhibit the remarkable capability of the approach presented for long-time simulations. Promising numerical results suggest the SDSCD is suitable for high-precision and long-time numerical simulations, as it has structure-preserving property and it can suppress effectively numerical dispersion when coarse grids are used. [ABSTRACT FROM AUTHOR]