Summary Using volume averaging we generalize Gassmann’s (1951) isotropic equation for fluid-filled porous media to solid-filled porous media with disconnected pores. This exact equation can be used as an analog of Gassmann's fluid substitution transform for solid-filled porous media, since it predicts the change in effective moduli upon solid substitution, depending only on porosity, elastic stiffness of frame and pore-solids, and initial effective stiffness. This solid substitution transform is exact if induced pore-stress field during a specific experiment is homogeneous. For all other cases, this equation is just an approximation, and has also been suggested by Ciz and Shapiro (2007). We note that this approximation does not always fall within rigorous solid substitution bounds, but under specified conditions, it is a strict bound on solid substitution. We therefore discuss the factors which govern the accuracy and applicability of this approximation. We also present a general solid substitution approximation which requires, in addition to porosity, at least one of the following: ultrasonic fluid filled un-drained modulus, saturated modulus with a hypothetical solid or crack porosity.