When hydrocarbon reservoirs undergo pressure depletion during production or pressure increase during fluid injection, the reservoir rock frame, as well as the rock mass above and below the reservoir, undergoes anisotropic stress changes. In most existing subsurface simulators, the change in rock stress is accounted for only via rock and fluid compressibilities; however, for more accurate fluid flow and rock mechanics modeling, a coupled geomechanics and fluid flow subsurface simulateor should be used. The work presented in this paper investigated developing a mathematical formulation using finite-difference techniques to solve the geomechanics' equations consistent with the mathematical formulation for solving fluid flow equations. The key considerations are consistency of the mathematical formulation (finite-difference technique) for both geomechanics and fluid flow calculations, and ease of implementing this formulation. The results show that it has successfully modeled the induced stress changes in the reservoir rock created by either fluid production or injection. In addition, the solution obtained from applying finite-difference technique in solving the geomechanics equations are comparable to that obtained from using finite-element techniques. Furthermore, the experience obtained from this work indicates that the adapted control volumes for fluid flow and geomechanics computations are well-structured and the developed formulation is computationally robust.