Wetting or dewetting on soft elastomeric surfaces is largely controlled by the dissipative properties (viscoelasticity) of the substrate. The component of liquid surface tension acting perpendicularly to the solid causes a deformation, or "wetting ridge", which must be displaced with the triple line. Previously, triple line motion due to capillary imbalance has been studied, whereas in the present work, we consider liquid motion due to gravity. Liquid drops running down an elastomeric plane move at a speed largely determined by the properties of the polymer. Results obtained agree well with the theory and demonstrate how motion depends on the state of the polymer, the angle of inclination of the plane, and drop volume.