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Vehicle manufacturers face mounting pressure to increase fuel economy and reduce vehicle tailpipe emissions in order to reduce the environmental impact of their vehicles and to meet ever more stringent regulations. Wrightbus have developed first generation single– and double–deck Hybrid Electric Vehicle (HEV) city buses, a number of which are in regular service in London and other cities. These buses utilise a series hybrid powertrain with a turbo-diesel engine, drive motors with total output powers between 120 kW and 170 kW and a DC electrical storage system. Fuel savings up to 30% have been achieved in service. This paper presents a literature review of hybrid vehicle modelling, and covers the work completed by Queen's University to create a software model of the Wrightbus HEV drivetrains in the Mathworks Mat-lab/Simulink environment. The model has been calibrated to several drivetrain configurations, including differing battery technologies, control systems and vehicle hardware.