Abstract: Based on the finite element analysis, the methods of design optimization and sensitivity analysis for the composite laminated plate structures with structural buckling stability as constraint or objective are studied. A dependence of critical buckling load sensitivity on the stress field and external loads is discussed in detail, and its different computational methods in the problems of the size, shape and stacking sequence optimizations are proposed. A design model for buckling stability optimization of the composite laminated plates is built, and the sequential linear programming (SLP) and sequential quadratic programming (SQP) are adopted to solve the optimization problem. The design model and solution methods proposed are available for complex structures with composite laminated plates and can also be combined with static, frequency and dynamic response optimization. The methods have been implemented in the software JIFEX for the finite element analysis and design optimization of general purpose structures. The numerical examples demonstrate the validation of the algorithm and program of the paper.