Abstract: This talk is about the finite element approximations of a poroelasticity model. To better describe the multi-physics process of deformation and diffusion for poro-elastic materials, we firstly present a reformulation of the original model by introducing two pseudo-pressures. We then propose a time-stepping algorithm which decouples the reformulated PDE problem at each time step into two sub-problems: one of which is a generalized Stokes problem for the displacement vector field (of the solid network of the poro-elastic material) along with one pseudo-pressure field and the other is a diffusion problem for the other pseudo-pressure field (of the solvent of the material). A practical advantage of the time-stepping algorithm allows one to use any convergent Stokes solver together with any convergent diffusion equation solver (and its code) to solve the poroelasticity model. Moreover, it is showed that the proposed formulation also has a built-in mechanism to overcome so-called “locking phenomenon” associated with the numerical approximations of the poroelasticity model. Numerical experiments are presented to show the performance of the proposed approach and methods and to demonstrate the absence of “locking phenomenon” in our numerical experiments.