The nonlinear properties of materials can couple with nonlinear geometries in component applications producing surprising overall system responses. Hence materials must be designed for particular, component level, applications, taking into account the component geometry, to achieve optimal performance. Here we focus on the compressive stress-strain and load-deflection characteristics of soft, polymeric foams in nonlinear geometries. The model system for these coupled nonlinearities is the thin layer of foam contained between two initially concentric spheres. We find that a nonlinear component-level response is exhibited with nonlinear geometries, even with a material whose compressive stress-strain response is linear. Polymeric foams exhibit a modified system-level response that is not apparent from standard viscometric testing results. The spherical geometries tend to concentrate the force in a more localized area of the foam, as opposed to the force distribution seen in linear materials, and this gives greater importance to the higher strain regions of the foam stress-strain response. In addition the geometry diminishes the contribution to the mechanical response in the low to middle range of the stress-strain response curve. These findings have provided critical insights to material designers who are engineering new generations of materials with enhanced component-level performance. (C) 2008 Wiley Periodicals, Inc.