We develop a method of determining the working lifetime of metal construction elements under hightemperature oxidation with periodic thermal loads. To estimate the damage to the metal resulting from both creep due to tensile stresses and fatigue due to periodic loading we chose the crit~5;on of extended durability and its refinement in the case of tensile equivalent loads and thermocycle shapes that vary in time in the oxidation process, We compute the working lifetime and exhib# the regularities of destructioa of steel pipes with a mass-isolated internal surface in a high-temperature oxidizing environment.The authors [1,7] have proposed a mathematical model of high-temperature oxidation of metals. In the original relations the results of experimental studies are taken into account more fully, in particular, the presence of a rather thick transition region between the oxidized film and the pure metal. The proposed model makes it possible to determine the time of final film oxide formation as a new phase and to study the regularities of the oxidation, as well as to compute more precisely the stress-strain state in the system at each stage from generation to flaking of the oxidized film as a function of the geometric and specific physical characteristics of a metal construction element.The loss of functioning of a metal element when high-temperature oxidation and thermocycling occurs may begin not only after the complete combustion of the metal, but significantly earlier. This may occur through the appearance of macrocracks, caused by the accumulation of damage in the metal due to both creep from the action of tensile stresses and fatigue from cyclic loading. For that reason, in this case the method of computing the longterm durability must be based on criteria that take account of the mutual influence of fatigue damage and long-term damage [4,5,8,9,11,13]. Under the action of tensile equivalent stresses o p that are constant in time and N cycles of constant shape the durability criterion can be written as follows [5]:Here (when equality holds) N is the maximum allowable number of cycles; N ~ is the number of cycles that cause a macrocrack without taking account of the effect of damage from creep; O,lr is the conditional limit of long-term strength (the tensile stresses that cause destruction of the construction element at a given temperature T after observation over time x; D and m are characteristics of the construction material. The parameter D takes account of the total damage from thermocycling and creep. We remark that for a large class of steels its value varies over the range 0.6 < D < 1. The parameter m > 1 depends strongly on the temperature. The number of cycles N ~ depends on the extent of the strains and can be estimated using the following formula [8]:Here Ae is the maximum possible range or-elastic strain intensity in a cycle; S and E are the resistance of the seams to tearing and the Young's modulus of the construction material. The equivalent stresses crp can be determined from the relation crp =ma...