This paper studies the application of the method of quadratic programming. By means of optimum design of integrally stiffened waffle shell and solution of dual prob1em of geometric programming using the method of quadratic programming，we have proposed the fol1owing methods: the variables substitution，the gradient travel mode for an improvement on initia1 expansion point，the restrieted step method and the modified Gauss elimination. Some simple and efficient methods are given for the utilization of the method for quadratic programming. The results obtained here Show that those approaches a1so have a good effect on convergence hastening and accuracy raising.