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The M-B fractal model was modified. The deformation properties of elastic stage, elastic-plastic stage and plastic stage of elastomer were analyzed. In the combination of macro and micro perspective, the fractal model of normal contact stiffness between two cylinders’ joint surfaces was established considering the influence of friction. And the influence of relevant parameters on the normal contact stiffness was revealed with the research of numerical simulation. The work had geometric characteristics and scale independence, which improved the fractal model of joint surfaces to a certain extent. Simulation works showed that normal contact stiffness increased with the increase of actual contact area and contact force, and decreased with the increase of normal load. And when the friction coefficient was less than 0.3, the normal contact stiffness showed linear attenuation with the increase of friction coefficient. When the friction coefficient was larger than 0.3, the normal contact stiffness showed exponential attenuation with the increase of friction coefficient.