In this article, the vibrating mode scanning polarization force microscope (VSPFM) is modeled with a spring-mass-damper system under van der Waals forces and polarization forces. The behaviors of VSPFM are analyzed numerically. Numerical analysis shows that by superimposing the long-range polarization interactions upon van der Waals forces, the tip motion can be greatly altered. Through adjusting the ac bias voltage between the conductive tip and dielectric substrate, the working regimes (intermittent contact or pure noncontact) of VSPFM can be controlled freely. The results also indicate that this kind of microscope is suitable for measuring mechanical properties of soft samples, where proper contact force is required. As an application example of VSPFM, the radial Young’s modulus of DNA is determined. It is found the measured DNA modulus increases as deformation increases. This trend is the same with that observed in measuring elastic moduli of thin soft films on hard substrates. The elastic modulus is about 300 MPa if the ratio of deformation to DNA diameter is less than 30%.