An analytical procedure is developed to design and predict the behavior of a pressure vessel. If a pressure vessel contains hydrogen, it is difficult to predict what will happen in the future. In this study, this is accounted for and the stress intensity factor for mode-Ι is calculated because the main factor controlling mass diffusion, as a driving force, is related to the stress in this mode. Also, it is known that the stress intensity factor depends upon concentration. The main challenge in hydrogen embrittlement is the prediction of crack growth and the estimation of lifetime for a pressure vessel. This paper investigates the effect of hydrogen diffusion upon crack in a pressure vessel by using numerical finite-element simulations. The fracture behavior of the alloy as related to hydrogen embrittlement was also studied. The computational simulations involved sequentially-coupled stress and mass-diffusion concentrations at the crack tip. Although there have been various previous works in this area, most of them have been experimental estimates of hydrogen diffusion. In this paper, we calculate the stress intensity factor by using the finite-element method (FEM) and use mathematical analysis simultaneously. The analytical method alone could not be used because the mass diffusion has special characteristics. That is, the treatment of diffusion is different at each step. We conducted finite-element modeling simulations of the intergranular fracture of alloy X-750 due to hydrogen embrittlement. Sequentially coupled stress and mass diffusion determinations were carried out in order to determine crack tip stresses and hydrogen diffusivity in the crack-tip region. Good qualitative agreement between the FEM modeling and the analysis was observed.