A stretchable undergarment comprises a one-piece body slimming unit made of front and rear panels cut and sewn along the edges to form a tubular body shaping garment construction which is stretchable in the longitudinal direction, and having a lightweight zippered opening along the front. The undergarment is made from a woven stretchable satin material containing a small amount of thin spandex-type elastic fibers forming a predominately one-way vertical stretch in a base textile fabric made from thin polymeric textile fibers such as nylon.