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Numerical analysis is carried out for a frictionless receding contact problem of a perfect-fit pin and bushing in a uniaxially loaded plate. The problem is analysed using the finite element method under the assumption of plane strain and linear elasticity. The problem is investigated for the influence of external load and for different geometries. The obtained contact pressures show uncharacteristic behaviour, where higher peak values occur on contact surfaces with larger contact angles. This seemingly contradicts not only the physics of receding contact problems, but also the physical laws of contact problems in general. It is shown that the reason for this unusual behaviour is, in fact, in the physical reduction of the contact area as the radius of curvature decreases. This class of problems shows to be linearly dependent on the intensity of load as regards the contact stresses, and load has no influence on the contact angles.