An overview of the most important formulations and numerical methods in the field of contact problem analysis is presented in this work, followed by an investigation of the behaviour of receding contact problems. The receding contact analysis was carried out for two different types of problems – the problem of a perfect-fit pin and bushing in a hole in a plate and the problem of an indenter pressing an unbonded layer resting on a substrate. The problems were analyzed using the finite element method within the scope of linear theory of elasticity and under the assumption of plane strain conditions. The numerical analyses were II carried out in the Femap software package, which uses the NX Nastran solver. Such contact problems were investigated for the influence of the intensity of external load, as well as the influence of different geometries and material properties. In the investigation of various materials a reference analysis was carried out for the case of material similarity between all the three bodies, after which material properties were varied in turn for each body. Finally the influence of friction was investigated as well. The obtained contact pressure distributions for the pin-bushing-plate problem show quite a unique behaviour, where higher peak values of contact pressures occur on contact surfaces with larger contact angles, which may seem very uncharacteristic not only for conventional contact problems, but for the class of receding contact problems as well. This class of problems shows to be linearly dependent on the intensity of external load, with negligible effect on the change of the contact angles. The problem of indenter, layer and substrate was investigated following the same methodology and the resulting influence of material dissimilarity and friction is systematically investigated here as well. This class of problems shows non-linear behaviour, where both the contact pressure distribution and contact half-width were found to be non-linearly dependable on the applied external load. Experimental investigation on steel models was carried out by optical measurements of displacements so as to ascertain the deformation behaviour of a layer indented into a substrate. The used method employs the digital image correlation technique and the ARAMIS 4M system was used in the experiment. The obtained measurement results show a satisfactory degree of agreement with the numerical results.