Abstract: In this talk, we will present a hybrid mixed finite element method for poroelasticity model. The hybrid P1-RT0-P0 discretization of the displacement-pressure-Darcy’s velocity system of Biot’s model presented is not uniformly stable with respect to the physical parameters, resulting in some issues in numerical simulations. To alleviate such problems,  we stabilize the hybrid scheme with face bubble functions and show the well-posedness with respect to physical and discretization parameters, which provide optimal error estimates of the stabilized method. We introduce a perturbation of the bilinear form of the displacement which allows for the elimination of the bubble functions. Together with eliminating Darcy’s velocity by hybridization, we obtain an eliminated system whose size is the same as the classical P1-RT0-P0 discretization. Based on the well-posedness of the eliminated system, we design block preconditioners that are parameter robust. Numerical experiments are presented to confirm the theoretical results of the stabilized scheme as well as the block preconditioners. We will also present some other works on poroelastic problem simply.