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The dispersion relation of the infinite long rod model with a weak interface has been deduced via wave equation of the guided waves and boundary spring interface model. The dispersion characteristics of the rigid interface and the slip interface are calculated, while the effect of different axial stiffness coefficient is also discussed. The results suggest that the phase velocity of the slip interface decreases slowly with increasing frequency at the low frequency of the L (0,1) mode. As for the weak interface, when the axial coefficient Kt is in the particular range of [1010,1014]pa/m, the interface turns from the slip interface to the rigid interface. That shows the value of axial coefficient Kt is an essential prerequisite for the non-destructive evaluation to evaluate the interface cementation degree.