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A mathematical model is presented that simulates belt tension forces in an automotive belt drive during rapid engine acceleration. The model is formulated as a base excitation problem in which the known motion of the crankshaft is used to excite the system. The elasticity of the belt is included by using linear elastic springs in the open spans and on the arc of contact of the belt with each pulley. The complete model includes the movement of the automatic tensioner arm, the variation of accessory load torques with speed, the effects of centrifugal tension, and the inertia of each component. A numerical example is presented which shows good agreement with experimental data. Similar results have been obtained for other cases tested.