In recent years, flexible wheels have been used in planetary exploration rover projects in order to increase traction capabilities of such vehicles. These flexible wheels can increase performance and prevent the rover from getting stuck in the soft terrains. These flexible wheel systems consist of a rigid hub which is connected to the flexible tire circumference through a number of radial springs. For simulation purposes, a model of such a system is developed using rigid body dynamics for the wheel hub motion and Euler-Bernoulli beam theory for the elastic deformation of the flexible tire tread. The contact between the flexible wheel and the soft soil is modelled using a volumetric contact model in form of an elastic Winkler foundation model. The equations of motion are derived using Lagrange's equations. To allow for faster simulations and future parameter optimization studies, a second non-dimensional model is developed and its validity is tested in a number of driving simulations.