In order to solve the conflict problem between the ride comfort and the road holding, the optimal design of shock absorber that minimizes the r.m.s. of sprung mass vertical acceleration and pitch rate with the understeer characteristics constraints in the high speed stability is proposed. The design of experiments and the nonlinear optimization algorithm are used together to obtain the optimal design of shock absorber. The second order regression models of the input variables(front and rear damping coefficients) and the output variables (ride comfort index and road holding one) are obtained by the central composite design in the design of experiments. Then the optimal design of shock absorber can be systematically adjusted with applying the nonlinear optimization algorithm to the obtained second order regression model. The frequency response analysis of sprung mass acceleration and pitch rate shows the effectiveness of the proposed optimal design of shock absorber in the sprung mass resonance range with the understeer characteristics constraints.