The paper describes possibilities to use industrially adhesive gripping elements in automatized handling processes especially for flat objects but also for objects slightly dissected according to height (e.g. sheets of glass, plastics, metals, plastic products etc.) which have dry, relatively clean, and smooth contact surfaces. It begins by analyzing results obtained in the field of designing combined vacuum-adhesive gripping elements, and the exclusively adhesive (passive) ones being suitable for technologically difficult handling conditions, e.g. in vacuum, as well. Furthermore, problems of the maximum carrying capacity of individual gripping elements being arranged parallel on a frame of a multi-element gripping head. A new concept of a compensation module of the gripping element position is presented as well, namely in relation to the head frame and to the handling object contact surface dissected according to height.