The paper analyses one of possibilities to use new materials based on polyurethane, polypropylene or silicone having highly adhesive contact surfaces for gripping elements designing. In concrete terms, it is a case of an alternative approach to the solution of designing standard multi-elements vacuum gripping heads with an active control system (vacuum level control) controlling gripping forces in processes of automatic handling flat objects of the plate type. The aim of this new design solution is to replace individual gripping elements (suction cups) by elements, the surfaces of which coming to the contact with the object handled are provided with adhesion materials. The system minimizing energy demands stemmed from this solution, namely in the way that it decreases or even eliminates the pressure air consumption when combined vacuum-adhesive or only adhesive gripping elements are used. Moreover, it is possible to use the adhesive gripping principle profitably in technological processes susceptible to the environment contamination with airflow when manufacturing new products with many functional layers. Besides a general analysis of problems, the paper presents outputs of laboratory tests. Also a computer model of the contact respecting rheological behaviour of the adhesive material basic matrix is given.