The friction force is effective for dissipating seismic energy. Therefore, in recent years, the installation of a frictional isolator in industrial facilities has been investigated. When a system including this isolator is regarded as multi-dof system, however, the seismic response of the system is obtained only by non-linear time history analysis. A great deal of time is required for non-linear analysis. In the present study, the easy estimation of seismic response for a multi-dof system with friction is considered. The seismic response of a multi-dof linear system can be obtained by the response spectrums method. This estimation is based on the modal analysis method. In the present paper, a method of modal separation for a 2-dof system with friction is presented. However, the accuracy of the proposed method depends on the mass ratio γ, the frequency ratio R_ƒ and the friction force. The proposed method is compared with 2-dof non-linear time history analysis, and the accuracy of the proposed method is calculated at γ ≤ 0.1 and R_ƒ ≤ 3. The present study defines the area within an error of 10% as the applicable area of the modal analysis method for a friction system and shows the range of error over 10%. The proposed method can be useful for obtaining the seismic response of a 2-dof friction system without non-linear time history analysis.