Abstract: The padded frame of a seat being upholstered rests on a support placing the back of the seat in vertical alignment under a carriage mounted on guides establishing a vertical freedom of movement of the carriage. The carriage has a cluster of resilient cantilever arms extending downward, each of the arms having a follower at the lower end adapted to move along the contour of the seat back. The cover for the seat back is slipped inside-out over the cluster of arms, and relative movement of the carriage toward the seat installs the cover outside-out. Other resilient arms in the cluster are preferably mounted on the frame of the machine, with relative movement provided by moving the seat unit with respect to the frame.