Abstract: This paper is concerned with the optimization design on critical loads of the nonliner stability of thin spherical shallow shells under the action of the unifonmed distributed loads.When the volum ν(β)of the shell and the geometric parameter f of the shell are given,varied thickness parameter β which makes the critcal loads of the shell a maxjmum or a minmimu can be solved,and the numerical results are plotted ih figure forms and table form.In addition to,this paper deals with the constraint optimization of the nonlinear bending problem of thin circular plate.