The strength of materials and structural elements operating in contact with high-pressure gaseous hydrogen is studied as applied to the problems of hydrogen power-generating industry. The requirements to the design of structural elements operating in hydrogen are formulated. We propose a model of influence of high-pressure gaseous hydrogen on the strength and plasticity characteristics of structural materials and apply this model to the development of the corresponding procedures of strength analysis and evaluation of the cyclic fatigue life and durability of strucrural elements of hydrogen power-generating equipment taking into account the dislocation and diffusion mechanisms of hydrogen transport in the metal. The data on the properties of materials in hydrogen, the choice of the proper safety and durability margins, and the evaluation of admissible stresses in the structures are presented. The analysis of strength, cyclic fatigue life, and the number of cycles to failure are illustrated by special examples.