Taking advantage of the probability function, we have analyzed the localization phenomenon of the solution of a propagating function under the condition that the propagation constants are randomly distributed. For example, we have investigated the localization phenomenon of the voltage wave for a transmission line in which the characteristic impedance is randomly distributed. We have confirmed that the localized solution is in existence on the random lossless transmission line. Even in the case that the voltage wave is impulsively excited by the current source, the voltage wave is localized. Because the light wave is seriously affected at the localized position in the lossy transmission line, we have determined that the light wave localization phenomena are generated by multi-reflection.