The most important information required for chatter stability analysis is the dynamics of the involved structures, i.e. the frequency response functions (FRFs) which are usually determined experimentally. In this study, the tool point FRF of a spindle-holder-tool assembly is analytically determined by using the receptance coupling and structural modification techniques. Timoshenko's beam model is used for increased accuracy. The spindle is also modeled analytically with elastic supports representing the bearings. The mathematical model is used to determine the effects of different parameters on the tool point FRF and to identify contact dynamics from experimental measurements. The applications of the model are demonstrated and the predictions are verified experimentally.