The best layup for a hybrid laminated cylindrical shell subject to a buckling load constraint is determined. The objective of the optimization is the minimum weight design of these structures. The ply angle is taken as the design variable. Various configurations of graphite and boron epoxy layers are considered in order to determine an optimal stacking sequence. The symbolic computational software package MATHEMATICA is used in the implementation and solution of the problem. this approach simplifies the computational procedure as well as the implementation of the analysis/optimization routine. Results are given illustrating the dependence of the optimal layup on the cylinder length and radius. It is shown that a general purpose computer algebra system like MATHEMATICA is well suited to solve structural design problems involving composite materials.