The dynamic behaviors of the joint interfaces make a great difference in machine tools, especially in high-end numerical control machines. To provide an assessment of the normal dynamic parameters in contact deformation of elastoplastic solid joint interfaces theoretically, a dynamic model of joint interfaces was proposed and studied. Based on contact fractal theory and contact-mechanics theory, interfacial parameters, including normal damping dissipation factor, stiffness and damping have been investigated, while the influences of the elastic, elastoplastic and fully plastic deformations of contacting asperities are considered. Solution for the force-displacement relationship in the elastoplastic regime is done by the well supported assumptions: the microcontact area and microcontact normal load are enforcing continuity between the elastic and fully plastic regimes. Numerical calculation results reveal the complications of nonlinear relation between normal contact load and normal dynamic parameters, including the normal stiffness, damping dissipation factor and damping over joint interfaces. Furthermore, normal dynamic parameters and fractal parameters, including fractal dimension D and fractal roughness parameter G also present complicated relationships.