Due to the complex material and shape of synchronous belt, it has complex mechanical behavior in normal operation. To solve this problem, propose a matrix model to calculate the tangential pressure of the meshing part between tooth and pulley. In the matrix model, use spring to replace the contact between synchronous belt and pulley, synchronous belt was discretized and separated into independent parts. In order to verify the model correctness, multi-body dynamics software RecurDyn was used to simulate the synchronous belt transmission system. The results show that the calculated results is closed to simulation results at the beginning and the end of the meshing part where the tangential pressure is larger, and there are some difference in the meshing part where the tangential pressure is smaller. Comparing with other methods, the matrix model has less computation, which solves the difficulty of calculating the tangential pressure of the belt, and provides a theoretical basis for the selection and design optimization of synchronous belt.