According to the considerable increase of the length of belt conveyors, the dynamic analysis of systme becomes necessary to consider the variation of tensions and transient motion of components during starting and stopping of conveyor. The mathematical model of system is derived using the lumped parameter method. The input driving force is represented with two functions of time and pulley speed to count the characteristics of motor and fluid coupling. An example system was studied with 14 km in the distance of carrying. At head, it has two drivers and one gravity take-up and at tail ond driver and one power winch take-up. In the example, the transient tensions and responses, calculated using two cases of driving force, are mutually compared in starting mode. Also, the position of maximum tension and the braking force of take-up are obtained in stopping mode.