The invention relates to a method and an apparatus for wrapping an article (30) with a web-like wrapping material. Said article is in one stage moved past wrapping means (3) while said wrapping means (3) provided with dispenser means (1) are rotated around said article (30) along a circular path in a first plane of rotation. In a further stage of wrapping said article is rotated by rotating means (15) in a second plane of rotation substantially normal to said first plane of rotation. Between said stages the surface of the wrapping material web is turned about 90° such that said surface of said web is always substantially normal to said planes of rotation in both stages.