Based on the surface impedance theory (SIT) and the coupled-wave theory (CWT), this paper has established the second-order transmission line equation applicable to coaxial resonators with corrugated inner conductor. By utilizing the equation, the resonant frequency, Q factor and field profiles geometry of the eigenmodes of coaxial resonators can be calculated in view of the mode coupling, and the variables of the slot width and depth in the coupling coefficient can also be applied to calculate their impact on the resonant frequency and Q factor. The numerical results show that, the slot width and depth have significant impact on the resonant frequency, but their effect on Q factor is approximately negligible.