This chapter discusses the problem of decomposing multi-objective optimization problems related to damping, Optimization of damping enables subtle tuning of a dynamic system to certain conditions the system is expected to work under. The process of optimization constitutes the art of creating a compromise between many factors defined by appropriate requirements. The mathematical description incorporated in this process most often reflects optimization and multi-objective optimization methods. An important problem is the global discussion of the whole optimization task related to the choice of damping characteristics that is, taking into consideration the fact that dynamic systems can work under different conditions and for different structural parameters. The aim of the analysis is multi-objective optimization of damping and elasticity characteristics of a linear model of a vehicle suspension system with two degrees of freedom. A kinematic stochastic interaction has to be taken into account as the external excitation coming from road roughness.