Apparatus for measuring the stiffness of mail articles on the principle of measuring deflection of a beam in bending comprises a rectilinear conveying portion for conveying the mail articles, a deflection roller disposed in a staggered offset manner between two wheels having deformable rims in such a manner as to form a substantially triangular peak on the rectilinear conveying portion, and an inlet ramp that is disposed upstream from the peak and that follows the upward slope of the peak.