研究了轴对称弹性环形薄板的两种优化问题，第一是在体积约束下极大化板的屈曲载荷。第二是在屈曲载荷约束下极小化板的体积。利用阶梯折算法和幂级数法得到问题的特征方程。最后求解两个非线性规划问题。通过数值结果的比较和分析，表明二种对偶优化问题的解是相互类同的。 Two kinds of optimization problems of axially symmetric elastic annular thin plates are studied. The first is the buckling load of the maximalized plates under the volume constraint. The second is to minimize the plate’s volume under buckling load constraints. The characteristic equation of the problem is obtained by the method of staircase conversion and power series. Finally solve two nonlinear programming problems. The comparison and analysis of numerical results show that the solutions of the two kinds of dual optimization problems are similar to each other.