A numerical method to solve the contact kinematic problems of elastic bar or circular micro-slip dry friction damper was proposed. Firstly, the damper and the time course of external excitation were discretized in the space and time domain respectively, and the same number of contact points was attached to the discrete damper. Secondly, the determination criterion of the contact kinematic state of the contact point pairs was used to each contact pair, and the stiffness matrix of the damper was modified. Thirdly, the whole balance equation with the new stiffness matrix was solved in each time step. Differing from the way the finite element software dealing with the contact problem with friction, the iteration was avoided, thus the feasibility of the solution was guaranteed. Meanwhile, the restriction of the distribution and the time variability of the normal load was overcome, and therefore it provided a more accurate boundary condition for solving dynamic response of structure. Lastly, the response of structures constrained by the macro-slip and micro-slip damper were computed by the MHBM (Multi Harmonic Balance Method) respectively and the distinctness of the solution was analyzed. Results show that the microslip model damper can have a broader normal force range for vibration reduction.