The physical parameters of the contact interfaces, such as preload and surface roughness quality, significantly affect the stiffness of joints. Knowledge of the relationship between these interface parameters and the equivalent stiffness allows joints to be considered in the design stages of complex structures. Hence, this paper considers the effect of contact interface parameters on the identified equivalent stiffness parameters of joint models. First, a new generic joint model is proposed to model the contact interfaces. Then, the ability of three different joint models, including the new model proposed in this paper, to capture the linear effects of contact interfaces under different preloads and surface roughness qualities is investigated. Finally, it is concluded that the preload and surface roughness quality control the normal and shearing stiffness of the joint models respectively. Experimental investigations also reveal that a complex mechanism governs the energy dissipation in the contact interface.