Starting from the fundamental equation theory of elasticity (Lamè), applied in the case of an elastic semi-space in the presence of a concentrated force, it is proposed to develop it for a uniformly distributed load characteristic of a screw-flange assembly. Expressions of spatial stresses resulting from tightening and limit conditions are proposed so that it is possible to determine the rigidity of the flanges. The proposed mathematical model allows both the calculation of the rigidity of the flanges in any configuration and the calculation of the rigidity of the clamping screws.