This paper deals with multiobjective optimization of symmetrically laminated composite truncated circular conical shells subjected to external uniform pressure load and thermal load. The design objective is the maximization of the weighted sum of the critical buckling load and fundamental frequency. The design variable is the fibre orientations in the layers. The performance index is formulated as the weighted sum of individual objectives in order to obtain optimal solutions of the design problem. The first-order shear deformation theory (FSDT) is used in the mathematical formulation of laminated truncated conical shells. Finally, the effect of different weighting factors, length-to-radius ratio, semi-cone angle and boundary conditions on the optimal design is investigated and the results are compared.