Abstract: To obtain the analytical expression of the optimal damping ratio in a 2 DOF linear model of vehicle suspension with zero mean white noise velocity input, making the acceleration of the suspension mass a minimum. Using the transfer function derived from the differential equation of the 2 DOF linear model of vehicle suspension, the special integral is worked out and the optimal damping ratio obtained by resolving for the extremum of the expression. During the deduction, the damping of the tire is neglected. The optimal damping ratio is merely the function of the vehicle structural parameters and has nothing to do with the running conditions. The expression can be used to estimate the suspension damping ratio in the preliminary design phase.