This monograph contains theoretical foundations of the spectral method for fatigue life determination where 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 being linear combinations of stress or strain components on the critical plane are analyzed. The formula proposed in this book enables to determine power spectral density of the equivalent history directly from the components of the power spectral density matrix of the multidimensional stochastic process. It presents the assumptions and the procedure of determination of basic relationships of the spectral method. The authors work out equations determining the fatigue life according to the spectral method using various linear hypotheses of fatigue damage accumulation. The algorithm of fatigue life contains five blocks: 1 determination of loading, 2 determination of the critical plane position for the assumed multiaxial fatigue failure criterion, 3 determination of power spectral density of the equivalent stress or strain, 4 determination of statistical parameters of the equivalent parameter responsible for fatigue damage, and 5 fatigue life calculation according to a suitable hypothesis of damage accumulation.