The typical contact between rotor disc and blade dovetail characterizes itself for being not merely normal, but also tangential, because of the complex load system applied to the blade. This fact has a great impact from the Fretting Fatigue point of view, because unexpected oscillating shear loads can lead to premature failures and service mishaps in gas turbine engines. In this work an analytical model is proposed to determine the tangential contact stiffness, assuming constant preapplied normal load and increasing tangential load. The system geometry is simplified and reduced to a bi-dimensional punch in contact with a flat body, accordingly with analytical theories found in literature.