A tabular reservoir, circular in plan, is located at depth parallel to the surface. Compaction of the reservoir as fluid is withdrawn causes a change in the stress and displacement fields in the surrounding medium. A solution to this problem is obtained by determining the boundary conditions at the interface between the reservoir and the half-space using Eshelby's <1957> cut-and-weld technique. The displacement field in the reservoir and the surrounding medium is then calculated using the reciprocal theorem. The displacement field is found to be the same as that calculated by Geertsma <1973a, 1973b> and by Segall <1992>Segall et al. <1994> using another technique.