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A fractal model of joint interfaces was established based on fractal contact theory. The elastic-plastic deformation of asperities was taken into account in the model. By numerical simulation, the nonlinear relationship between the contact force and the real contact area was obtained,，as well as the effects of elastic-plastic deformation on the contact of joint interfaces. The result showed that the contact force increased nearly linearly with the real contact area. The contact force decreased due to the increase of fractal roughness parameter G with the same contact area, but complicatedly varies with the fractal dimension D. The share of elastic-plastic contact area decreased with the increase of real contact area, increased with the increase of G, and complicatedly varies with D. The share of elastic-plastic was large enough and can not be ignored. It decreased with the increase of D.When the elastic-plastic deformation was overlooked, the contact fore was slightly larger than the results involved the elastic-plastic deformation. The error percentage lied within the range 5%～60%, which decreased with the increase of D.