A process for the shaping of the side surface of a metal body or container (10) such as an aerosol or a beverage bottle for food or technical use, obtained by progressive deformation operating steps of its side surface carried out in sequence on a machine having an intermittent rotating table, an opposite alternate translatory motion plate, a loading drum, gripping pliers of the bodies, deformation and possibly embossing and/or debossing tools and an unloading drum of the same bodies, the process including the steps: feeding the bodies (10) on the machine provided with an intermittent rotating table and of an opposite translatory motion plate; gripping the bodies along a limited area (12) between 10.0 and 35.0 mm, of their side surface from the bottom with a fixed or an axially rotating gripping plier; carrying out a broad deformation (18) on the side surface of the bodies (10) with tools working from the inner and/or outer part of the same bodies.