The design of a passenger car’s ride and handling goals requires an enormous amount of hardware and prototypes. To avoid time-consuming testing activities, one crucial trend is the virtualisation of suspension development. Another goal of the virtualisation is the determination of vehicle properties at an early stage of the development process. Highly accurate suspension models are required to transfer the full vehicle’s characteristics into simulation tools. Since the jounce bumper is an important component of the suspension system, modelling its functional behaviour is essential for virtualised chassis development. Therefore, two dynamic modelling approaches are derived and compared in this contribution. One approach is based on local linear model networks and thus can be seen as a grey box model. The other approach consists of white box rheological elements, which allow the physical interpretability of the model parameters. The comparison of the approaches is based on experimental parameter identification, which includes synthetic and real excitations recorded on representative roads. The advantages of the proposed approaches will be discussed in terms of their suitability for the virtual design of the driving behaviour.