The main objective of this paper is to establish a consistent geometrical frame focusing oil the coupling between hydro-mechanical aspects. An arbitrary Lagrangian and Eulerian method (ALE) has been used to deal with the numerical simulation for oil/water flow in deforming porous media. When the mesh motion is equal to the velocity of the deformed porous media, the convection term referred to as the relative velocity between fluid flow and the skeleton deformation is removed from the Finite Element Method (FEM) formula. Therefore, some difficulty in FEM numerical simulation has been solved. A classical oil/water flow coupled with solid deformation is simulated by ALE code with an iterative scheme. An ALE with a fully implicit and sequential iterative algorithm [Implicit Pressure Explicit Saturation (IMPES) method], which calculates the oil phase pressure and water phase saturation with least squares FEM, is used to simulate the oil/water two-phase fluid flow. Compared with general reservoir simulation, the ALE method could reach a consistent frame description or a more rigorous definition of the parameters for the solid phase and the flow phase. This may be very important for larger deformations in stratum induced by petroleum production and tracking the moving interface in multi-phase fluid flow.