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The seismic response of a structural system equipped with friction-type energy dissipation devices is generally nonlinear. The main reason for this nonlinearity is the friction mechanism that possesses two possible motion states, referred to as stick and slip states. The essential force and kinematic conditions of a friction damper, in these two states, are different. In this paper, by employing a state-space formulation and a linear integration scheme, the discrete-time solution of dynamic response of a structural system equipped with multiple friction devices, which can be in either a stick or slip state, was derived in a single and unified form. The nonlinear friction forces, in each time step of analysis, were solved by satisfying both the force and kinematic conditions of certain motion states. Based on a derived discrete-time solution, a numerical analysis procedure was proposed, which allows the time interval of analysis to remain constant, even at the transition of stick and slip states; thus, it is a systematic and efficient method for numerical implementation. The solution of the method was compared with the analytical free-vibration response of a single DOF system, and also with the harmonic and seismic responses simulated by other conventional numerical methods. These examples demonstrate the accuracy and stability of the proposed method.