This work presentes new directions in the modelling and approximation theory for the problem of saturated flows in rigid and linear elastic porous media. The following aspects are emphasized. - Presentation of a systematic and consistent theory to describe the problem that generalizes the classical theory, wich, based on experimental observations, expresses the momentum balance for the fluid by Darcy s law. - Derivation of error estimates of finite element approximation of seepage in porous elastic media. In this area we emphasize the Biot s model of consolidation. Sequential post-processing techniques are proposed to improve the rates os convergence of pore pressure and effective stress approximations.