The apparatus comprises a quadrangular frame on which a vehicle to be repaired can be fixed by means of appropriate templates. The frame is rigidly associated with a pantograph mechanism capable of raising and lowering it to the required distance from the ground. Longitudinal guide elements for at least one movable carriage are fixed to the frame, and a support for a device for tensioning the damaged bodywork is pivoted to the carriage and can rotate on a substantially horizontal plate. At least one pair of wheeled vehicle-holder crosspieces are slidable on the frame and are associated with adjustable-height wheeled elements. Each crosspiece has two jacks for lifting and positioning a vehicle on the templates.