A belt transmission model with dry or partially wet belt models used for dynamic analysis has been presented in this paper. A two-dimensional discrete model was created, consisting of rigid elements connected with each other by means of longitudinal and torsional spring-damping elements (SDEs). 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. Motion of the transmission is triggered under the influence of torque loads applied on the pulleys. Calculations results are presented of reaction, contact and friction forces acting on dry and partially wet belt. Finally, an example of using the model to analyse the dynamics of a wet automotive belt transmission system driving the alternator and coolant pump has been presented.