This paper presents the implementation of a vehicle and powertrain model of the parallel hybrid electric vehicle which can be used for several purposes: as a model for estimating fuel consumption, as a model for estimating performance, and as a control model for the hybrid powertrain optimisation. The model is specified as a multi-domain physical model in MATLAB Simscape, which captures the key electrical, mechanical and thermal energy flows in the vehicles. By applying hand crafted boundary conditions, this model can be simulated either in the forwards or backwards direction, and it can easily be simplified as required to address specific control problems.Modelling in the forwards direction, the driver inputs are specified, and the vehicle response is the model output. In the backwards direction, the vehicle velocity as a function of time is the specified input, and the engine torque, and fuel consumption are the model outputs.The model represents a parallel hybrid vehicle, which is being developed in the TC48 project. The project goal is to produce a prototype of a plug-in parallel hybrid system which is integrated into existing front wheel drive powertrains with modest additional engineering, cost, volume, and mass requirements.This paper explains the motivation for the project, and presents examples of the simulations which were used to guide the design. The vehicle simulation models used to evaluate the layout options are described and discussed. Sensitivity analyses are presented which informed the design decisions.A novel use of the Simscape component of MATLAB/Simulink which allows the same model structure to be used for both forwards and backwards simulations is demonstrated. This method has the possibility for more general application, and a toolbox is being developed which assists the generation of mathematical models of this type.