Solid shaft is a common case in technical practice including interference fit couplings. Thick walled cylinders theory, which is used in interference fits computation, leads to wrong values of stress in case of solid shafts at the inner side. A numerical simulation using smaller and smaller ratios of the radii demonstrate a tendency towards stress homogeneity. Particularly along the axis of the shaft, the theory of stress under axial – symmetrical loading, analytically validates the numerical data. Practical consequences are very important as maximum admitted pressure is computed on the basis of equivalent stress. New checking formulae are proposed for interference fit couplings, containing the specific case of the solid shaft.