This paper presents a comprehensive model to capture the in-plane dynamics of a motorcycle system to evaluate the quality of its vibration isolation, and the design of an engine mount system. The model consists of two main structural components, the frame and the swing-arm, as well as the power-train assembly, engine mounts connecting the power-train to the frame, and the front-end assembly. The model accounts for frame and swing-arm flexibility using reduced order finite-element models. The power-train assembly is modelled as a rigid body connected to the frame through the engine mounts and to the swing-arm through a shaft assembly. The engine mounts are modelled as tri-axial spring-damper systems, and the front-end assembly is modelled as a lumped mass. The complete vehicle model is used to solve the engine mount optimisation problem, so as to minimise the total force transmitted to the frame while meeting packaging and other constraints. The mount system parameters – stiffness, position and orientation vectors – are used as design variables for the optimisation problem. The imposed loads include forces and moments due to engine imbalance as well as loads transmitted due to high amplitude, low frequency bump loads, through the tyre patch. Since packaging constraints play a significant role in a motorcycle layout, it is, therefore, important to determine the displacement envelope of the power-train under extreme loading conditions to ensure clearance with other components around the power-train. A motorcycle mount system should ideally be able to isolate the frame under steady-state loading conditions and at the same time limit the maximum excursion of the power-train under transient loading conditions.