Themonographisdevotedtothespectralmethodfordeterminationoffatigue life of machine elements and structures under multiaxial service loading. A detailed review of literature on spectral methods that includes: publications describing various relations between histories of loading and power spectral density functions, some methods of fatigue life determination under Ga- sian loading and under multiaxial service loading has been presented in the monograph. The monograph contains theoretical foundations of the spectral method for fatigue life determination. The authors have discussed a rule of description of random loading states with the matrix of power spectral d- sity functions of the stress/strain tensor components. Some chosen criteria of multiaxial fatigue failure being linear combinations of stress or strain com- nents on the critical plane have been analyzed. The proposed formula enables to determine power spectral density of the equivalent history directly from the components of the power spectral density matrix of the multidimensional shastic process. The assumptions and the procedure of determination of basic relationships of the spectral method according to stress and strain - proacheshavebeen presented. The authors workedout equations determining the fatiguelife accordingto the spectralmethod using various linear hypot- ses of fatigue damage accumulation.