<p>Modular mesh antennas consist of multiple nearly identical hexagonal-frustum modules that stretch the cable networks from stowed configuration into a parabolic reflector surface. The deployable truss, a multi-loop closed-chain mechanism, determines the deployment path through its member parameters, which directly affect the efficiency of unfolding the cable network. Traditional design approaches focus on folding ratio and motion compatibility, but often neglect load-driving efficiency and the ease of deployment. This paper presents an analytical model for evaluating the deployability of modular mesh antennas, accurately capturing the deployment load by fully considering the material and geometric nonlinearities in cable networks. A parameter optimization methodology is introduced for the deployable truss to improve the efficiency of unfolding cable networks. Rod lengths are used as design variables, required driving force as the objective function, and folding ratio, motion compatibility, and surface accuracy are included as constraints. The results show that the driving force required for the optimized configuration is greatly reduced compared with the original configuration. Two prototypes were fabricated and tested, confirming the effectiveness of the optimization in improving the deployability of modular mesh antennas.</p>