A belt transmission model used for analysing the dynamics of such a transmission has been presented in this paper. A two-dimensional discrete model was adopted, consisting of rigid elements connected with each other by means of longitudinal and torsional spring-damping elements (SDEs). For the belt-pulley contact, a special contact model and a dry friction model were adopted. The belt-pulley contact phenomena were described with the use of a model with appropriate stiffness and damping between the contacting surfaces and a simplified Threlfall friction model was used to describe the friction phenomenon. The transmission motion caused by a force-type input or a kinematic input applied to transmission pulleys was examined. Results of determining the reaction forces developing in the belt and the normal and friction forces between the belt element and the pulley, arising from the driving and resistance torques on the pulleys, have been given as an example in the subsequent part of this article for the belt transmission adopted. Finally, an example of using the model to analyse the dynamics of an automotive belt transmission system driving the alternator and coolant pump has been presented.