The pseudospectral method is a high-accuracy numerical modelling technique which requires less memory and CPU time than traditional numerical modelling techniques, such as finite difference. However, full 3-D modelling is still computationally intensive. As we must compromise between realism and computational efficiency, we have developed a 2.5-D pseudospectral scheme for calculating 3-D elastic wavefields in media varying in two dimensions. To demonstrate the feasibility of the scheme described in this paper, we use data from a refraction survey carried out in 1984 by the Explosion Seismology Group in the southeastern foothills of the Hidaka Mountains, Hokkaido, Japan.