In this study, the effects of power spectrum density of strains on the fatigue life of a pressure vessel steel were examined with random loading fatigue tests. Different three types of the power spectrum density of strains, S ₁ (symmetrical, single peak shaped), S ₂ (unsymmetrical, single peak shaped) and S ₃ (two peaks shaped) were used. One problem in a comparative discussion of the fatigue life by a random loading with that by a constant amplitude loading is the definition or representative expression of the fatigue life under random loading. In this paper, a new expression N_{f (rep)} was defined with the idea of representative frequency. It was found that the fatigue life corresponding to different strains spectrum could be put in order in a lump with r. m. s. value of strains by using the N_{f (rep)} . In the same way, the constant amplitude fatigue data and the random fatigue data were compared with each other using N_{f (rep)} and r. m. s. value of strains, showing a good agreement. The life estimating method TYPE 1 on the basis of r. m. s. value of strains and N_{f (rep)} was proposed. Mean hysteresis energy W newly defined. W corresponding to a particular r. m. s. value of strains showed a little lower value (about 90%) in the random fatigue test than in the constant amplitude fatigue test. Both of the constant amplitude test data and the random fatigue test data were plotted on a log-log coordinate, and each data were located on two lines which had a same slant and the distance of them was about 0.80 in terms of life ratio. The life estimating method was newly proposed, TYPE 2 obtained on the basis of W and N_{f (rep)} . Comparing the two proposed methods, TYPE 1 is much easier to apply, and TYPE 2 needs more information although it gives more precise estimation. In addition, verification of the Miner's law was also done using three kinds of wave counting methods, i. e, the range count, the hysteresis loop count and the peak count method. As a result, it was found that a proper counting method had to be selected according to the r. m. s. value of strains for application of the Miner's law.