The effect of periodic overstressing on fatigue crack propagation was studied with sharp notched specimens of a low carbon steel, and the result was discussed in the light of the linear cumulative damage concept. A very small number of cycles of overstress applied intermittently during a very large number of cycling of understress had an extremely detrimental effect; namely, they yielded a remarkable acceleration of crack propagation (about one hundred times) and a very small value of the cumulative cycle ratio (less than one hundredth). Fractographic examinations revealed that the mechanism of crack propagation under the periodic overstressing was quite different from that under steady stress conditions, consistently with the high rate of crack propagation. Questions were raised on the conventional fatigue design based on the results with smooth specimens under steady loads, and also on the way of presenting the fatigue test data under program loads based on the modified Miner type laws.