The method provides a loose wrap on an article. A sheet of thin, flexible wrapping material is positioned around the article. A projecting flexible excess portion is formed as an outwardly projecting bubble in the wrapping material that is positioned around the article. The wrapping material is then sealed around the article while the bubble portion is maintained in the wrapping material. The apparatus comprises various mechanisms for effecting the method steps. The assembly is particularly useful in a wrapping machine. The combination used in conjunction with a wrapping machine includes a pocket mechanism for holding the article having the thin, flexible material wrapped therearound. The projecting bubble portion is formed by an assembly disposed adjacent the pocket mechanism. The pocket mechanism includes a side wall member having an indentation to receive the projecting bubble portion formed in the wrapping material. The bubble portion forming assembly includes a backing member disposed adjacent the side wall member of the pocket assembly and has a shaped supporting surface against which the bubble portion is conformed in shape.