A fully coupled two-phase flow and geomechanics in a reservoir system is considered. The governing equation is derived in terms of the saturation, pressure, velocity for the flow and displacement for the structure. A nonlinear computational scheme is constructed by incorporating the mixed finite element with the conforming element, and the corresponding finite element procedure is proposed, which guarantees the local conservation of mass within the element. The effectiveness and correctness are verified by performing the numerical experiment for the water flooding in a homogeneous reservoir. Moreover, the water flooding in a heterogeneous reservoir with cross fracture is simulated and the high resolution of saturation solution is obtained, showing that the complex multiphysics of the reservoir system can be well captured by the proposed method.