The sensitivity of the ride characteristics of a road vehicle to the mechanical characteristics of the bushings used in its suspension is discussed here. First, the development and computational implementation, on a multibody dynamics environment, of a constitutive relation to model bushing elements associated with mechanical joints is presented. Bushings are made of a rubber type of material, which presents a nonlinear and viscoelastic relationship between the forces and moments and their corresponding displacements and rotations. Suitable bushing models for vehicle multibody models must be accurate and computationally efficient, leading to more reliable models. The bushing is modeled in a multibody code as an arrangement of springs that penalize the motion between the bodies connected. In the methodology proposed here, a finite element model of the bushing is developed in the framework of a finite element (FE) code to obtain the curves of displacement/rotation versus force/moment for different loading cases. The basic ingredients of the multibody model are the same vectors and points relations used to define kinematic constraints in any multibody formulation. Spherical, cylindrical and revolute bushing joints are developed and implemented in this work, since the methodology is demonstrated through the ride over bumps, at different speeds, of two multibody models of a road vehicle: one with perfect kinematic joints, for the suspension sub-systems; the other with bushing joints, riding. Then, sensitivities of different vehicle kinematic responses to the characteristics of the bushings used in the suspension are evaluated, by using numerical sensitivities. Based on the sensitivity analysis, indications on how to modify the vehicle response by modifying the bushing characteristics are drawn.