The paper deals with modelling of transport energy demand related to an electric vehicle (EV) fleet. The main aim of the paper is to provide a proper methodology of deriving a simple transport energy demand model aimed to be used within: (i) real-time control of EV fleet charging, (ii) planning of EV fleet routes, and (iii) various EV fleet-related techno-economic analysis studies. The model is represented by maps also known as response surfaces, which are obtained by simulating the considered EV model over synthetic driving cycles. The synthetic driving cycles are introduced to replace a high number of recorded driving cycles in a statistically representative way, thus reducing the number of time-consuming EV simulations. The final transport energy demand model is validated against the more precise energy consumption data obtained by simulating EREV model over the full set of recorded driving cycle.