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Nonlinear constitutive relations for the fluid-saturated porous elastic solid with isotropic pore structure undergoing pure mechanical large deformations are developed. The fluid-solid composition is considered as the immiscible mixture consisting of physically identifiable constituents preserving its own individual, physical properties during deformation process. Considerations are based on the balance equation for the internal energy of the whole composition which is required to be satisfied identically by the internal energy constitutive functions postulated for particular components independently. Constitutive relations for partial stresses of particular constituents are obtained, and the internal equilibrium condition for the whole composition is established. These relations for the media with incompressible matrix material and for nonsaturated porous skeleton are discussed.