In this article we develop an analytical theory that correlates the macroscopic curvature of stressed film/substrate systems with the microscopic in-plane and out-of-plane deflections of planar rotators. We have extended these stress-deflection relations in the case of nonlinear stress fields and validated the results with the aid of finite element simulations. We use this theory to study the heteroepitaxial growth of cubic silicon carbide on silicon (100) and discovered that, due to defects generated on the silicon substrate during the carbonization process, wafer curvature techniques alone may not enable determination of the stress field in the grown films either quantitatively or qualitatively.