Two parameters expression of probability density function of the stress response power spectrum was adopted to predict the multiaxial random vibration fatigue life with a couple of fatigue failure criterions. A train battery box structure was studied by this method with MSC Fatigue software. After comparing different multiaxial random vibration fatigue life in the different stochastic processes including broadband and narrowband,the different fatigue failure evaluation criterions including the maximum principal stress criterion,the equivalent stress criterion and the critical surface criterion,the conclusion shows that using broadband distribution and the clinical surface criterion to predict the multiaxial random vibration fatigue life is more reasonable.