A wrapping machine for wrapping groups of products with an extensible plastic film to form bundles includes a conveyor for supporting and moving a group of products along an advancing direction inside the wrapping machine, a supporting device for supporting the group of products received from the conveyor, a wrapping unit for wrapping a portion of film around the group of products, supported by the supporting device, in order to form a bundle, and a supplying unit to supply the wrapping unit with the film portion separated from the film. The supporting device includes a gripping device that holds an initial flap of the film portion during the wrapping of the group of products, a containment device to abut against the group of products to guide the products when moved along the advancing direction through the wrapping unit and/or to support and restrain the group of products during wrapping.