Abstarct: Atomic Force Microscope (AFM) is one of the powerful and useful tools in nanoscale science with applications from surface topography and characterization differents material. In this paper Vibrations of Cantilever beam is Considered, which tip isn't matching on the center of cross-sectional exactly.The Equation of motion and boundary conditions are considered using nonlocal theory and Hamiltons principle.The General formulation for resonance frequency and sensivity is obtained. The comparison of the present results and The state which The tip matches on the center of cross-sectional exactly is presented.The Results show that the effect of distance from center of cross-sectional is very important and should be considered for achiving The better results.