An apparatus for conveying viscous material from a drum-like container with a container bottom and a circumferential container wall extending from the container bottom to a container upper side and being open at the container upper side has, for closing the container a follower plate having a material outlet attached to a conveyor pump. The follower plate has an annularly circumferential wiper ring that has a radially outwardly extending contacting part for contact against an inside face, turned toward the follower plate, of the container wall. The contacting part can be pressurized with a variable pressing force for pressing against the inside face (36) of the container wall. The follower plate is mounted by moans of at least one vertically extending retaining rod on a horizontally extending crosspiece mounted on or close to a first end on a lifting device for raising and lowering of the crosspiece. Its second end is free.