Timing belt systems, usually consisting of a toothed belt and multiple pulleys, are used in many mechanical devices, especially in the internal combustion engine to synchronize the rotation of the crankshafts and the camshafts. When the system operates, the belt teeth will be transmitted by the pulley teeth meshed with them. Timing belt drives can make sure that the engine' s valves open and close properly due to their precise transmission ratio. In this thesis, a quasi-static computational model is developed to calculate the belt load distributions and the torques around pulleys for different timing belt systems. The simplest system is a two-pulley system with one oval pulley and one circular pulley. This computational model is then extended to a two-pulley system with one special-shaped pulley and finally generalized to determine the load conditions for a multi-pulley system with multiple special-shaped pulleys. Belt tooth deflections, tooth loads, belt tension distributions, friction forces, and the effect of friction hysteresis have been taken into consideration. Results of these quantities are solved by a nested numerical iteration method. Periodic torques generated by the varied radius of noncircular pulley are calculated by this computational model to cancel the undesired external cyclic torque, which will increase the life of timing belts. / Master of Science / Timing belt systems, usually consisting of a toothed belt and multiple pulleys, are used in many mechanical devices, especially in the internal combustion engine to synchronize the rotation of the crankshafts and the camshafts. When the system operates, the belt teeth will be transmitted by the pulley teeth meshed with them. Timing belt drives can make sure that the engines valves open and close properly due to their precise transmission ratio. In this thesis, a quasi-static computational model is developed to calculate the belt load distributions and the torques around pulleys for different timing belt systems. The simplest system is a two-pulley system with one oval pulley and one circular pulley. This computational model is then extended to a two-pulley system with one special-shaped pulley and finally generalized to determine the load conditions for a multi-pulley system with multiple special-shaped pulleys. Belt tooth deflections, tooth loads, belt tension distributions, friction forces, and the effect of friction hysteresis have been taken into consideration. Results of these quantities are solved by a nested numerical iteration method. Periodic torques generated by the varied radius of noncircular pulley are calculated by this computational model to cancel the undesired external cyclic torque, which will increase the life of timing belts.