When the atomic force microscope cantilever in tapping-mode is vibrated at a frequency close to its fundamental resonance frequency, the tip on its free end will be close to and away from the sample periodically. The higher harmonic signals produced by non-linear interactions between the tip and sample surface contain more nanomechanical information. We study the influence on the contact time by different elastic modulus and the relationship between higher harmonic amplitude and contact time. By theoretical analysis and calculation, we obtain the law of characterizing the sample surface elastic difference with the higher harmonic amplitude. Moreover, we obtain the experimental result consistent with the theory, on our homemade higher harmonic system.