In order to simulate the cavity growth of an underground gasifier in thin seams at great depth, Wilks1 has developed an original model that solves the continuity equation in the horizontal plane with the hypothesis of radial fluid flow around the injection well. In the model presented here, the continuity equation in the horizontal plane has been taken into account, removing the limiting assumption on flow (radial direction) assumed by Wilks. The simultaneous solution of the continuity equation and the Darcy law has been carried out using the Boundary Element Method (BEM); this method is particularly suitable for solving problems where boundary conditions are of prime importance. The model enables the influences of the permeability of the medium and gasifier geometry to be demonstrated.