A gift wrapping enclosure encloses a gift which has been inserted within an interior of a main body formed of flexible material. An end portion of the main body surrounding an open end is folded back to form a cuff. An interior surface is exposed at the cuff, and the exposed cuff surface has a different color, texture or material characteristic from the main body. The main body is constricted at the cuff to close the open end and confine the gift, and is expanded at the cuff to provide access to the interior to remove the gift.