We propose a new numerical method for the mechanical coupling of the deformation of a fluid-rock system. The method is based on coupling the lattice Bhatnagar-Gross-Krook method for fluid flow with an elastic lattice method for static and dynamic deformation, which allows for the inclusion of arbitrary heterogeneity in the elastic properties of the solid and arbitrary fluid-filled conduit geometries. The scheme permits the simulation of the interaction of a heterogeneous elastic solid (dynamic and static deformation) with fluid motion (fluid flow and/or acoustic waves). This scheme is completely discrete and does not involve a priori continuum equations of state. The method has been validated against the reciprocal theorem for fluid-structure interactions. We provide two examples where the scheme is used to model two possible source mechanisms for the generation of seismic waves, an explosion in a fluid-filled conduit and pressure equilibrating across two adjacent fluid reservoirs.