A device for massaging either a human hand or a human foot includes a number of massage elements formed on a plate that is moved within a carriage adjacently below an opening in a housing. The sole of the foot or the palm of the hand is held in contact with the massage elements or in contact with a flexible sheet extending within the opening by an enclosure. In one version, separate enclosures are provided for the hand and for the foot; in another version, the enclosure is adjustable for use with either a hand or a foot.