The currently used design methodology for polymeric matrix composites (PMCs) is based on the assumption of linear elastic stress-strain behavior of the composite. In certain composites such as carbon-epoxy and carbonpolyimide, and for certain lay-ups, laminate stress-strain curves are found to be highly nonlinear, especially at elevated temperatures. Exposure to oxygen and moisture can further enhance this nonlinearity due to constituent material property changes and increased micromechanical damage. In such materials and environments, use of linear stress analysis methods can result in inaccurate results, and thereby less than satisfactory designs.