The fluid-mechanical coupling is known as the effect of both the porous media in a fluid as the fluid in porous media, it has been studied intensively in past years and in recent years, given its importance in various application fields of engineering. This works studies numerical models of coupled deformation and flow, considering coupled two-phase flow and deformation, taking into account the nonlinear soil behavior. The numerical analysis of two-phase flow can lead to instabilities due to parabolic-hyperbolic character of the governing equations and the method employed does not adequately capture the heterogeneity of the geological environment. Thus, we analyze the numerical formulations capable of overcoming these difficulties and to be employed on coupled condition with deformation. Initially the finite element method, FEM, is employed for solution of the coupled two-phase flow problem. Another formulation is employed in a mixed basis, the pressure equation is solved through the FEM, solution of the equation of saturation by finite volume method, FVM, using interpolation scheme with high order to capture the saturation front. In an intermediate step, it is employing methods to better pos-processing the velocity filed as the lowest-order Raviart- Thomas finite elements. Finally, it is presented a formulation that employs the discontinuous finite element method, DFEM, presented in Hoteit et al (2008), is coupled in this work with the problem of deformation using a staggered procedure for iterative solution of the systems. Examples are presented that validate the various formulations and highlight the properties of each formulation, with advantages and disadvantages in their applications.