The purpose of the study is to investigate the influence of porosity and void size on equivalent geotechnical engineering properties. The paper uses random field theory to generate models of geomaterials containing spatially random voids with controlled porosity and void size. Analyses then use finite elements and Monte-Carlo simulations, where each simulation leads to an effective value of the property under investigation. The effective value is defined as the property that would have led to the same response if the geomaterial had been homogeneous. Although the methodology can be applied to a variety of soil properties, the paper concentrates on elastic stiffness. A novel finite element model is developed involving “tied freedoms” that allows analysis of an ideal element test and hence direct evaluation of the effective Young’s modulus and Poisson’s ratio. A foundation problem of a footing on an elastic foundation containing voids is also described.