Abstract: Individual packages of individual sterile gloves have a glove holder with glove cuff holding means surrounding an opening in the holder in which the glove is positioned. A bottom cover secured to the holder extends across the side of the opening faced by the outside of the glove while a top cover extends across the side of the opening faced by the inside of the glove. The covers keep the glove in sterile condition during handling and storage of the glove packages. A glove package is inserted into a loading area of the gloving apparatus, either manually or automatically, and the glove package is moved to position over an opening into a vacuum chamber. During such movement the top cover of the package is opened. When over the opening to the vacuum chamber, vacuum is applied to the chamber to cause the bottom cover to open and the glove to be drawn into the chamber and inflated. A user now easily inserts his hands into the inflated glove, vacuum is released and the gloved hand is removed.