In this study, filament wound truncated cones under axial compression are with the objectives of minimizing the total weight and maximizing the failure load, which is defined as the minimum of the buckling and the first-ply failure (FPF) loads. The numerical results are obtained using an axisymmetric degenerated shell element based on a refined first-order shear deformable shell theory and a 2D degenerated shell element is used for verification purposes. It is shown that, FPF is more critical than buckling for thicker cones with lower cone angles.Optimal designs, where FPF and buckling are imposed as design constraints, are presented for filament wound cones using Micro-Genetic Algorithms. The results show that, using more layers having different winding angles has negligible influence on the failure load and the optimal design is not FPF critical for moderate levels of axial compression. The influence of the rotational boundary conditions on the optimal failure load is also demonstrated.