Media that present discontinuities as fractures and faults in a rock mass or oil reservoirs impose some difficulties in numerical simulation using standard Finite Element Method. One of these difficulties is the need for very refined mesh generation, especially in the region near the discontinuities, to obtain a reliable answer of the model, which can consume significant time. At the same time, the discretization of the discontinuity with very small elements compared to the rest of the model may lead to an increase in simulation time. This work presents the formulation of an element that is crossed by a discontinuity for use in coupling fluid-mechanical problems in single fluid saturated mediums. The insertion of the discontinuity in the element is obtained by adding new terms in the interpolation function, which eliminates its discretization. These additional terms can reproduce the change in the displacement and pore pressure field in the element due to the presence of discontinuity. The response of the element is validated by comparing it with one dimensional analytical solution and simple examples simulated in a commercial program.