On the basis of the energy approach of fracture mechanics, we develop a computational model of propagation of fatigue cracks in thin-walled hydrogenated welded joints under the conditions of plane stressed state. A problem of diffusion with the corresponding boundary conditions for the analysis of the field of hydrogen concentration in the zone of welded joint in the case of variable temperature is posed and its numerical solution is found. It is shown that the computed kinetic diagrams of fatigue fracture are in good agreement with the available experimental data. The relations obtained by using the proposed model enable us to predict the path and the period of subcritical growth of fatigue cracks.