The basic goal of this study is to find an alternate, more efficient method of simulating stochastic stress histories for fatigue analysis. Stress histories are generated from power spectral densities made up of either one or two rectangular blocks. The currently popular simulation technique produces a normal signal by summing sine waves with random phase angles. The fatigue damage predicted from stress histories simulated by this method is used as the basis of comparison for three other techniques. Two techniques which simulate correlated, Rayleigh distributed peaks and valleys are investigated. Another technique produces correlated peaks which have S. O. Rice's peak distribution. The rainflow method of cycle counting is used to determine the stress ranges from all the stress histories and Miner's rule is used to predict fatigue damage. It is concluded that fatigue damage from processes having single block power spectral densities can be efficiently and accurately predicted from a sequence of correlated peaks which have the peak distribution. This technique is three to four times faster than the currently popular technique. Simulation techniques which generate Rayleigh distributed peaks are found to be overly conservative in their prediction of fatigue damage. None of the three techniques investigated can be used for simulation of processes with two block power spectral densities. It is also concluded that a stress process cannot be sufficiently characterized solely by the spectral width parameter for fatigue damage predictions.