Abstract: Aiming at the problems of tangential displacement response of common used pre-tightening lap joints under tangential displacement excitation in engineering, a new slip force density distribution function based on actual morphological parameters and material performance parameters was proposed. The tangential response constitutive model of lap joint was obtained by using the distribution function, and the hysteresis curve and energy dissipation value per loading cycle were obtained. Compared with the published experimental results, it is found that the simulation value was consistent with the experimental, which proves the rationality of the model. Based on this, the relationship between the tangential displacement of the joint surface and the tangential force, tangential contact stiffness, and energy dissipation was studied. The results showed that the model could well describe the relationship between tangential force and tangential displacement. The trend of critical slip force function rise rapidly and then converges to zero after reaching its maximum value. The tangential force and tangential displacement show a non-linear characteristic, and with the increase of tangential displacement, the tangential contact stiffness shows softening phenomenon; the initial tangential stiffness is related to normal load, roughness parameters and plastic index. For a given contact surface, the greater normal force is given, the greater initial tangential stiffness is observed; the initial tangential stiffness also increases with the increase of plastic index.