Damping in built-up structures is often caused by energy dissipation or energy loss due to micro-slip along frictional interfaces interaction, which provides a beneficial damping mechanism and plays an important role in the dynamics vibration behavior of such structures, especially the contact stiffness and damping coefficient accounting for the kinematics joint. A detailed study the mechanics derived from the interaction interface between the different components has some embarrassment. And a careful study on the micro-slip phenomenon has been carried out using the finite element method. A classical joint configuration, the plane translation joint, has been used as the model problems. The focus of this paper is to evaluate the effect of dry friction coefficient, the external mechanics on the damping response of frictional joint interfaces interaction, to understand the evolution of the slip-stick regions along a joint interface during loading, and to quantify the amount of energy dissipation/loss during cyclic loading and its dependence on structural and loading parameters.