A study on the force transmission from a drive pulley to a belt is presented. The problem of belt slip on the drive pulley is often encountered when small slips initiate at the vanishing point of belt contact with the pulley and extend to the entire range of contact. This phenomenon cannot be satisfactorily explained by the conventional theory. Taking into consideration the elastic deformation of the lagging and the belt cover rubber which exists between the pulley and the belt cord for transmission of the driving force, the formulas for belt tension and the "slip ratio" which shows the range of the small slip are proposed for the design of the belt conveyor