This paper describes three procedures for calculating design derivatives of the nonlinear critical load. Constraints on the critical load arise naturally in optimal design of structures having nonlinear behavior. The incremental procedures used for nonlinear analysis can fail before reaching the final load level due to buckling or collapse of the structure. Therefore, load carrying capability of the structure must be improved before optimal design process can proceed further. This requires design derivatives of the critical load factor. A very simple and effective procedure among the three derived, is selected. It uses most of the information already calculated during analysis and sensitivity analysis of other constraints. Design sensitivity analysis is verified using two known examples. Several other structures are optimized to show effectiveness of the procedure. The sensitivity analysis can be combined with other constraints to optimize structures with more general requirements.