This paper concerns the optimal mass - to - stiffness ratio design of class-2 tensegrity towers. For different loading scenarios, the procedure seeks the topology and geometry of the structure that yields an optimal design satisfying common constraints. The domain of feasible tensegrity geometries is denned by imposing tensegrity equilibrium conditions on both unloaded and loaded structure. Remaining constraints include strength constraints for all elements of the structure and buckling constraints for bars. The symmetry of the design is imposed by restricting the domain of geometric variables and element parameters. The static response of the structure is computed by using a nonlinear large displacement model. The problem is cast in the form of a nonlinear program. The influence of material parameters on the optimal shape of the structure is investigated.