A method to calculate the Von Mises stresses in structures subjected to random loads is presented in this paper. The proposed method gives the exact values of Von Mises stresses in white noise random vibration loads and as accurate as desired in non-uniform random vibration. The method is quite efficient from the numerical point of view and has no limits from the size of the finite element model other than the capacity of the computer for standard normal mode vibration analysis. Exact reliability of the Von Mises stress is found and an extremely simple practical structural design criteria based on reliability analysis is proposed.