The article provides a dynamic model for belt conveyor. Based on the drive-force of conveyor,take-uptension of take-up assembly, gravity of conveyor belt and material, and friction between belt and idlers, it gives aviscoelastic dynamic equation for conveyor belt.It presents a calculation method of analytic solution to bothviscoelastic dynamic equation and geometric dynamic equation when automatic take-up assembly is applied to beltconveyor. The article also makes a study of design method of limiting and eliminating the conveyor belt’s elasticvibration.