This paper deals with the optimal design of an antagonistically actuated X-shape Snelson tensegrity mechanism to be used in a preliminary bird neck model made of a series of cascaded such mechanisms. The mechanism, subject to its own weight and to the weight of the subsequent mechanisms, is designed to maximize its wrench feasible workspace under given maximal actuation forces. Moreover, the mechanism is constrained to stand in a prescribed rest configuration. The optimized parameters are the link lengths and the springs stiffness.