Poroelasticity is a branch of continuum mechanics [1] which deals with the complex interaction between a deformable porous solid matrix and the flow of fluids trough the interconnected porous volume space. Within the poromechanical framework, a variety of problems spanning various fields are addressed, ranging from its original application in geomechanics, to contemporary challenges in biomechanics. The associated coupled boundary value problem is inherently complex and, for actual problem solution, computational approaches are needed. A multitude of finite element formulations are available in the scientific literature, most of them are concerned with two field discretization, namely solid displacement and pore pressure, or more elaborate three field discretization which mostly include displacements as one of the variable, therefore specific stabilization procedure are often needed in order to achieve accurate solutions. The proposed contribution present a new finite element approach, which is founded on a stress-based formulation [2], extended to the linear poroelastic context. As a starting point, a variational principle is established, wherein Cauchy stress and pore pressure serve as principal fields to be discretized. A few element types are introduced and implemented in an open Finite Element Program (FEAP). Their performance are examined on classical benchmark problems for poroelasticity, with stress accuracy being evaluated as a main feature of the proposed approach. A two-dimensional problem of a biological tissue is analyzed and the results discussed. Possible future extension to finite strain context is traced and discussed as a final remark.