The study presents a mathematical model for calculating the strength of a steel vertical cylindrical tank based on the elastic beam theory. The oil and gas sector uses similar tanks to store petroleum products and crude oil. An oil tank's depressurization can have detrimental effects up to a major disaster, which makes determining its strength a relevant problem. The factors to consider are not only the operating loads but also the negative effects of hydrogen formation resulting from electrochemical processes on the steel surface. The stress–strain state of a steel tank under the impact of static oil pressure is determined. The dependences of maximum mechanical stresses in the tank on the level of liquid in it and on the stiffness of the elastic foundation under it are constructed. The calculated stresses in the tank are used to evaluate the influence of hydrogen on the mechanical properties of the material. It is assumed that when the tensile stress threshold is exceeded in the tank, the metal is weakened through damage accumulation, this leads to a decrease in its effective modulus of elasticity. The calculation of the hydrogen-weakened tank is performed by determining the zones and depth of hydrogen degradation in the material and calculating the resulting stresses.