A compact machine for applying and contour milling or cutting of edge strips or laminates at the narrow sides of plate-shaped workpieces, in a forward cycle and a reverse cycle, with a single operator location and in continuously travelling manner, with a single conveying device at which the plates are transversely arranged such that the respective leading narrow side is arranged perpendicularly with respect to a longitudinal, main axis of travel, and the respective plate overhangingly extends from the conveying device for access, as well as being secured by clamps. The apparatus also includes an edge-gluing device and a shaping-milling device, both of which, with respect to the longitudinal axis, are sequentially arranged laterally at the conveying device. The apparatus further includes at least one milling or cutting tool or unit, which extends with its axis of rotation transversely with respect to the main axis, as well as parallel with respect to the plane of the workpiece and which is at least capable of operatively contacting and contouringly engaging the upper side of the workpiece. At the conclusion of travel of the workpiece at the shaping-milling device, the milling unit is lowered, the direction of travel of the conveying device is reversed and during the return thereof, the milling unit is operatively engagingly moved along the lower side of the workpiece.