The problem to be treated in this thesis is to obtain optimum values of equivalent spring and damper coefficients in the suspension of a weapon vehicle system in order to minimize the bullet-land dispersion at shooting. The dynamic model used is formulated as a 5 degree-of-freedom system when shooting without running and as a 4 degree-of-freedom system when running without shooting. Constraints on the magnitude of acceleration of the driver and recoil force are imposed. Displacement input from wavy road conditions has been included in the formulation. A computer program based on a steepest descent algorithm has been developed and used in the solution of test problems. The bullet-land dispersion at the optimum design is reduced by about 10\% as compared with that at an estimated initial design.