The concise description of one- and multidimensional stationary and non stationary vehicle loading histories for fatigue analysis using stochastic process theory is presented in this study. The load history is considered to have stationary random and nonstationary mean and variance content. The stationary variations are represented by a class of time series referred to as Autoregressive Moving Average (ARMA) models, while a Fourier series is used to account for the variation of the mean and variance. Due to the use of random phase angles in the Fourier series, an ensemble of mean and variance variations is obtained. The methods of nonparametric statistics are used to determine the success of the modeling of nonstationarity. Justification of the method is obtained through comparison of rainflow cycle distributions and resulting fatigue lives of original and simulated loadings. Due to the relatively small number of Fourier coefficients needed together with the use of ARMA models, a concise description of complex loadings is achieved. The overall frequency content and sequential information of the load history is statistically preserved. An ensemble of load histories can be constructed on-line with minimal computer storage capacity as used in testing equipment. The method can be used in a diversity of fields where a concise representation of random loadings is desired.