This monograph examines the theoretical foundations of the spectral method for fatigue life determination. The authors discuss a rule of description of random loading states with the matrix of power spectral density functions of the stress/strain tensor components. Some chosen criteria of multiaxial fatigue failure are analyzed. The formula proposed in this book enables readers to determine power spectral density of the equivalent history directly from the components of the power spectral density matrix of the multidimensional stochastic process.