As vehicle testing on existing vehicles is both time and resource consuming, the work of testing safety algorithms on vehicle is desired to be made more efficient. Therefore the goal of this thesis is to study and develop a vehicle simulation model that can simulate desired dynamics of existing and non-existing vehicles. The developed model consist of two areas of application: slow dynamics and vibrational dynamics. These areas are developed and validated using different methods, but as a part of the simulator, they are to be simulated together. For the slow, low frequency, vehicle motion, a three state transient motion model is derived and examined. The possibility of parametrisation is studied and performed using prediction error minimisation. For the vibration, high frequency model, a combination of a linear quarter car model with wheel motion is used to estimate road vibration characteristics. The modelled road is used to simulate the vehicle behaviour. The suggested methods regarding the vibration modelling and road estimation are performed using power spectral density as the road is not known determinately. Wheel speeds are used to study the power spectral densities as they are available at high sampling frequencies. The available tools and sensors used during this thesis are limited to existing vehicle sensors and GPS signals. The effect of this limitation is studied and the results are discussed.