This paper demonstrates a procedure to design an optimal mass to stiffness ratio tensegrity structure. Starting from an initial layout of the structure that defines an allowed set of element connections, the procedure defines positions of the nodal points of the structure, volumes of the elements and their rest lengths yielding a tensegrity structure having smaller compliance for a given load applied then an initial design. To satisfy design requirements strength constraint for all the elements of the structure, buckling constraint for bar elements as well as constraint on geometry of the structure are imposed yielding a nonconvex nonlinear constrained optimization problem. Structural static response is computed using complete nonlinear large displacement model. Examples showing optimal layout of a 2D and 3D structure are shown.