Compressive load capacity of composite lattice structures are studied. The objective of this research is to investigate the buckling strength of composite lattice structures and to design the most weight efficient structure with the highest buckling load. Buckling strength of both the composite lattice cylindrical and conical shells under axial compressive loads are examined. The main emphasis is placed on the effects of geometric constraints and the optimal design of the structures.In this research, various constraints are studied and the optimal structure which gives the highest strength to weight ratio is obtained. Moreover, these structures can be constructed by filament winding, the manufacturing process can be automated, and the costs can be greatly reduced.