This paper analyzes the small strain elasticity of fluid saturated porous media and the influence of the fluid static pressure, or pore pressure, on their isotropic constitutive properties. The porous medium is modelled as a lattice assembly of monodisperse spheres that interact through Hertz contacts. The size of the spheres and hence the matrix volume at zero solids stress are shown to be influenced by the pore pressure. Consequently, the structural pressure generated by elastic Hertzian contact deformations is shown to depend on both the volume occupied by the matrix and the pore pressure. This result is then generalized for random assemblies of spheres by using an isotropic constitutive law that is realistic for dry sands. The present findings suggest that the contributions of pore pressure and structural pressure to the total stress do not have a constant weighting as is often assumed, but one that is sensitive to the deformation state of the matrix. The theory also captures the characteristic loss of matrix stiffness during liquefaction at sufficiently elevated pore pressures. ©1997 American Institute of Physics.