Remarkable dependency of fatigue properties on speed, and that it is closey related to the internal friction in the specimen, were shown from testing several kinds of steels by means of the High Speed Fatigue Testing Machine developed by the author, as described in the 1st and 2nd reports. A model concerning the preyield plastic microstrain was developed here to explain the mechanism of this dependency of fatigue on speed, and from the analysis of this model subjected to periodical stress, the similer tendency in the amplitude-dependency and the speed-dependency of internal friction with those experimentally obtained was exhibited. From this, the model developed here may be considered to be acceptable. Next, the speed-dependency of fatigue obtained from the analysis, assuming that a certain amount of plastic strain is required to cause fatigue in the specimen as could be supposed from the expermental results, also shows the similer behavior with that experimentally obtained. Hence it could be concluded that the speed-dependency of fatigue is due to the time lag of the preyield plastic microstrain.