We investigate the steady configuration of a visco-elastic belt drive and its loss of stability under varying driving speed. The belt is considered as a linearly visco-elastic slender beam with small bending stiffness. Due to the presence of the small damping parameter and the small bending stiffness, the equations of motion are severly singularly perturbed. By variation of system parameters, like the driving speed, the damping coefficient, the tension force and the radius of the drums, we calculate the steady configuration and the stability limit of the belt. Preliminary calculations show, that the viscous damping, the distributed load and the strong bending at the drums can decrease the critical driving speed significantly and lead to flutter oscillations.