a b s t r a c tA multi-modal analysis on the intermittent contact between an atomic force microscope (AFM) with a soft sample is presented. The intermittent contact induces the participation of the higher modes into the motion and various subharmonic motions are shown. The AFM tip mass enhances the coupling of different modes. The AFM tip mass is modeled by the Dirac delta function and the coupling effects are analyzed via the Galerkin method. The necessity of applying multi-modal analysis to the intermittent contact problem is demonstrated. Unlike the impact oscillator model which assumes the impact/contact time is infinitesimal, the contact time can be a significant fractional portion in each cycle, especially for the soft sample case and thus results in different dynamic behavior from that of an impact oscillator.