The relation between the twisting fatigue strength and the bending fatigue strength varies with temperatures and specimen sizes, in addition to notches, flaws, and environments. In the present paper, the size effect on fatigue strength is discussed by calculating the probability of the flaws on the surface which affect the fatigue strength of materials, being considered that the fatigue failure of materials without flaws obeys the maximum shearing stress theory. And fatigue tests are carried out under bending and twisting moments at elevated temperatures and at a low temperature for smooth specimens and also for notched specimens. These results and the various past experimental results are adopted to the size effect discussed above, the following are explained in a unified form : the relation of size effect under bending fatigue and under twisting fatigue, the size effect of smooth specimens and notched specimens, the effects of flaws, specimen sizes, environments, and temperatures on the fatigue strength and notch factor, and the distribution of the fatigue strengths for various sizes of specimens.