In order to solve the modeling problems of saturated porous media, the engineering mixture theory was used to formulate the bulk constitutive theoretical framework of saturated porous media. Firstly, Supposing that the bulk deformation works of porous solid and fluid matrix were mutually independent and using Terzaghi’s effective spherical stress and pore pressure and fluid matrix pressure as stress state variables of constitutive model, the bulk stains expressions of solid phase and solid matrix and fluid matrix were obtained in the complementary energy.Secondly, the solid and fluid bulk constitutive equations of saturated porous cubes of balsawood in the loading and unloading stages were founded on the basis of the measuring data of model test conducted by Lade and de Boer. The calculating formulae of mechanical parameters were deduced such as solid bulk tangent modulus, Biot’s tangent coefficient and fluid Biot’s tangent modulus and so on. The change rules of mechanical parameters along with Terzaghi’s effective spherical stress and pore pressure were analyzed in the loading stage for solid bulk tangent modulus,Biot’s tangent coefficient and fluid Biot’s tangent modulus and so on. Finally, the one-dimensional consolidation equation of saturated porous media was derived from the bulk constitutive models of the paper and static balance equation. The consolidation behaviors of saturated porous cubes of balsawood were numerically analyzed and the change curves of consolidation degree and settlement with time were obtained. The researches show that, the solid bulk tangent modulus increased along with Terzaghi’s effective spherical stress and decreased along with pore pressure. The Biot’s tangent coefficient was between 0.42～0.95 and decreased along with Terzaghi’s effective spherical stress and pore pressure. The fluid Biot’s tangent modulus decreased firstly and then increased with Terzaghi’s effective spherical stress, and decreased with the increase of pore pressure. The tangent coefficient of pore pressure was less than 1.0 in most cases. The initial pore pressure was not equal to the external load in saturated porous media considering the compressibility of solid matrix. Thus the immediate settlement exists in saturated porous media after external load was applied. The modeling method in the paper can be used to model and numerically analyze nonlinear saturated porous media.