Optimum laminate configuration for minimum weight of filament–wound laminated conical shells subject to buckling load constraint is investigated. In the case of a laminated conical shell the thickness and the ply orientation (the design variables) are functions of the shell coordinates, influencing both the buckling load and its weight. These effects complicate the optimization problem considerably. The first level of complexity is attributed to the correlation between the volume and the buckling load and their dependence on the fiber configuration. The second level of complexity is associated with the high computational cost involved in calculation of the buckling load. Thus, the main objective of this study is to solve the optimization problem as well as to reduce the computational cost associated with it. Based on the characteristic buckling behavior of laminated conical shells the usual penalty function method is used.