This paper concerns optimization of prestress of a tensegrity structure to achieve the optimal mixed dynamic and control performance. A linearized dynamic model of the structure is derived. The force density variables that parameterize prestress of the structure appear linearly in the model. The feasible region of these parameters is defined in terms of the extreme directions of the prestress cone. Several properties of the problem are established inside the feasible region of the parameters. The problem is solved using a gradient method that provides a monotonic decrease of the objective function inside the feasible region. A numerical example of a cantilevered planar tensegrity beam is shown.