A three-dimensional elastic lattice method for the simulation of seismic waves is presented. The model consists of particles arranged on a cubic lattice which interact through a central force term and a bond-bending force. Particle disturbances are followed through space by numerically solving their equations of motion. A vacuum free-surface boundary condition is implicit in the method. We demonstrate that a numerical implementation of the method is capable of modelling seismic wave propagation with complex topography. This is achieved by comparing the scheme against a finite-difference solution to the elastodynamic wave equation. The results indicate that the scheme offers an alternative 3D method for modelling wave propagation in the presence of strong topography and subsurface heterogeneity. We apply the method to seismic wave propagation on Mount Etna to illustrate its applicability in modelling a physical system.