The robustness of mechanical systems is influenced by various factors. Their effects must be understood for designing robust systems. This paper proposes a model for describing the relationships among functional requirements, structural characteristics, design parameters and uncontrollable variables of nonlinear systems. With this model, the sensitivity of systems was analyzed to formulate a system sensitivity index and robust sensitivity matrix to determine the importance of the factors in relation to the robustness of systems. Based on the robust design principle, an optimization model was developed. Combining this optimization model and the Taguchi method for robust design, an analysis was carried out to reveal the characteristics of the systems. For a nonlinear mechanical system, relationships among structural characteristics of the system, design parameters, and uncontrollable variables can be formulated as a mathematical function. The characteristics of the system determine how design parameters affect the functional requirements of the system. Consequently, they affect the distribution of system performance functions. Nonlinearity of the system can facilitate the selection of design parameters to achieve the required functional requirements.