Starting from homogeneous scalar Helmholtz's equations associated with Borgnis p otential function in a cylindrical coordinate system, and based on the standing wave concept of slow-wave introduced in the paper, the analytic expressions of the dispersion relation and field distribution for azimuthally symmetric transverse magnetic modes in the resonant cavity chain with full-cavity terminations are derived, by using boundary conditions for Borgnis potential function in conjunction with field matching conditions at the common interface between adjacent sub regions. The resonance frequency of the four-cavity transit-time tube oscillator calculated by this analytic method is compared with that measured in experiment s and it is found that they are in agreement quite well. The field distribution of the oscillator developed by this analytic method is agreeable to that simula ted by numerical code.