The present work is concerned with the development and the validation of a model to evaluate the average and the variance of the fatigue damage in structures subjected to random loading. The technique of the approximation of these statistics through of the expansion into Taylor series was applied to the set of equations that describe the epsilon-N method and the Palmgren-Miner rule. The proposed model allows the evaluation of the statistical behavior of the notch stress ranges, of the notch strain ranges and of the cumulative fatigue damage. The developed model allows the combination of random factors associated to loading histories and to the behavior of the material. In other words, the model estimates the dispersion of the fatigue damage under an extensive aspect, quatifying separately the contributions derives from the dispersion associated to sources of variation of the material behavior and the loading histories. In order to evaluate the proposed model, 20 random loading histories were combined to two levels of dispersion of the material properties. The combination allowed the study of the model under several situations. The performance of the model was evaluated by comparisons with the Monte Carlo technique. The agreement of the proposed model with the Monte Carlo technique was considered good. An extensive study was realized concerning the influence of the random loading on the dispersion of the damage prediction. It was observed that the dispersion is strongly associated to sample s size. From the cases studied it was observed that sample s blocks with less than 3000 peak might conduct to dispersions larger than 10 per cent, for strictly stationary processes, and larger than 20 per cent, for wide-sense stationary processes. After studying the statistical behavior of the cumulative fatigue damage and of its critical value to initiate a fatigue crack, two analytical model for fatigue reliability analysis were presented. These models are developed under the assumption that cumulative fatigue damage and its critical value follow a lognormal or a Weibull distribution. To verify the predicted results the Monte Carlo analysis was used. From this analysis it was verified tha the interference statistical model, based on a lognormal distribution, describes better the behavior of the fatigue s reliability.