We use a finite element method to study the elastic properties of dry sandstone morphologies. We show that the dry Poisson's (Vp/Vs) ratio becomes independent of the Poisson's ratio of the solid phase at a critical porosity and that this limiting behaviour holds for any number of solid phases and is insensitive to the manner in which the phases are distributed. We represent the behaviour of the Poisson's ratio as a simple flow diagram and present an empirical structure-property relationship that holds for all Sandstone Morphologies independent of the number of phases and the Poisson's ratio of the solid phase.