This paper presents a theory and applications to account for changes in the fundamental, buckling, and post-buckling states when design parameters of a composite material are modified. The influence of micro-mechanical parameters (the volume fraction and the fiber orientation) and of cross-sectional dimensions is investigated. A numerical example for columns made of composite materials is presented. Sensitivity is studied for local buckling loads. Explicit expressions are obtained for the sensitivities in the form of perturbation expansions. A beam under transverse load is also investigated, and geometric design parameters employed to investigate sensitivity. The information from the sensitivity analysis can be used to improve a design by modification of the buckling load.