This paper describes some numerical experiments for stress modeling in the zone around a reservoir in a sedimentary basin, where oil and gas exploration is real or potential. We aim to map mainly low- and high-pressure zones, under the principle that they act as push-and-pull natural pumps for fluid accumulation. The necessary data for practical work is based on seismic data, as a post-migration process with the knowledge of velocities of the P and S waves, and the density information. The computation is designed for simple geometries to represent a reservoir geology, and it is addressed as a boundary value problem (BVP) involving the Beltrami-Michell's partial differential equation with Dirichlet conditions. The method employed was the Green's function expressed by Fourier series for the solution of the BVP, where the boundary conditions are given by the stress components along the boundary of the target volume. The first stress invariant controls the elastic mechanical behavior of the subsoil; therefore, once the distribution of rock pressure is obtained, and the boundary conditions are defined, solving the BVP allows the calculation of the stress components distribution (normal and tangential) within a separate target volume for details. The relationship between rock pressure and stress components is established by the Beltrami-Michell problem, which takes the form of a Poisson's equation. The proposed method was applied in a more complex target zone present in the Marmousi model, which contains reservoirs within regions of interest, expanding to more realistic complex problems.