In this paper, we investigate the propagation of high-frequency current waves along a stochastic transmission line inside a rectangular cavity using as basis the model of a transmission line with the symmetry of the resonator. The stochastization of the line is created by a stochastically arranged chain of loads. Using similar models one also can take into account stochastic geometry of the line. Research has shown a significant difference between the propagation of the current wave along the transmission line with stochastic loads in free space and in the resonator. In the first case, the average square of the absolute value of the transmission coefficient exponentially tends to zero with increasing length of the line due to interference phenomena for current waves. In the second case, in the average, the current can penetrate through the stochastic chain of the loads due to the re-reflection of the signal from the walls of the resonator.