Abstract: To obtain an approximate solution with the method ofweighted residuals, the perturbation method with plate center deflection asperturbation parameter is used to turn nonlinear partial differential equationsfor large deflection of rectangular plate to linear partial differentialequations. Then, a solution is obtained with the least square method. In thecourse of solution, an ascending power trial function family is used, which can beconditioned by the control parameter f. The results agree with theexperimental ones. Compared with previous researches, the precision ofcalculation is improved evidently. It is an effective method to obtain a besttrial function and a best approximate value.