In this study, in order to perform dynamic design of machine tools reasonably and effectively, a method was formulated to be applicable to the damped structures connected by joints having elasticity and damping by using substructure synthesis method. And a nonlinear solution method was proposed and it formulates the nonlinear parts by describing functions and uses the reducing transformation matrix by the substructure synthesis method. The results of frequency response analysis of a machine tool, where an NC lathe was partitioned by three parts of spindle, housing and bed-base part and the nonlinearity of bearing parts between spindle and housing was modelled, showed force dependency of the response.