In this paper, a new modeling approach is proposed to represent the tangential frictional stick-slip behaviors of contact interfaces in mechanical systems considering the surface fractal feature and normal loading conditions. Initially, surrogate asperities are defined to express the fractal feature of contact surface topography and the normal load of interface, and Jenkins elements are used to describe the tangential stick-slip motions between surrogate contact asperities. Then, a geometric series distribution principle of the normal loads at contact asperities is proposed to determine the yield forces of the Jenkins elements. The criterion for identifying the micro- and macro-slips of the contact interfaces is proposed, which are determined by the stick and slip conditions of the largest contact spot. An experimental setup for measuring the frictional stick-slip of contact interfaces is constructed, upon which tangential quasi-static experiments are conducted. Satisfactory agreements between the theoretical and experimental results indicate that the proposed modeling approach can perfectly predict the stick-slip behavior of contact interfaces. Finally, mechanical characteristics of the contact interfaces are investigated in detail by employing the validated modeling approach. Owing to the definite physical significance of the proposed modeling approach, the mechanism of the tangential stick-slip behavior of contact interfaces is partially demonstrated.