Medium-density rigid polyurethane (PU) foams are often produced in sealed molds; therefore, the processes inside the mold and structure of the produced foam blocks need to be understood. The structural and mechanical anisotropy is shown to be the third variable along with (1) concentration of the nanoclay filler and (2) density, to determine the mechanical properties of the filled PU foam composites produced in a sealed mold. The varying anisotropy of the specimens hinders the accurate evaluation of the filling effect. The methodology for the estimation of the anisotropy characteristics of specimens from different locations within the nanoclay filled PU foam blocks is elaborated. A criterion, based on analysis of Poisson’s ratios, is formulated for the selection of specimens with similar anisotropy characteristics. The shear and bulk moduli are estimated theoretically, dependent on the filler’s concentration, using the experimentally determined constants.