Abstract: When a tracked vehicle runs on a rough road surface, the vehicle body usually undergoes strong vibration, which significantly affects the working environment of the combat personnel and the shooting accuracy during the motion. Therefore, the vibration control of the vehicle body is much required. In this paper, a nonlinear stochastic optimal vibration control strategy for the electromechanical suspension of a torsional tracked vehicle with consideration of the actuator saturation is proposed. Firstly, the nonlinear stochastic dynamic model of the suspension system is built based on the space structure of the torsional bar and the nonlinear model of the air spring. Then, based on the stochastic dynamical programming principle, the dynamical programming equation of the electromechanical suspension system is established. The optimal bounded control strategy is formulated by solving the dynamical programming equation with consideration of the saturation of the actuator. Finally, the effectiveness of the proposed control strategy is evaluated by comparing the statistics of the responses of optimally controlled and uncontrolled systems. The influence of the time-delay on the control effectiveness is also discussed. Numerical results show that the proposed control strategy can effectively mitigate the nonlinear stochastic vibration of the electromechanical suspension, and the control strategy is found to be quite robust against the variations of the system parameters. To ensure the effectiveness of the control force, the time delay should be controlled within 0.15 second.