Abstract <p>The long-term destruction of a long thin-walled cylindrical shell during creep under conditions of a non-stationary complex stress state that takes into account the influence of the active medium is studied. The influence of the active medium on the creep and long-term strength of the shell is determined by the diffusion penetration of medium elements into the shell material. Using the kinetic theory by Yu. Rabotnov, we have determined the destruction time of such a shell under unsteady loading. A singular linear fractional model of creep and long-term strength, in which the ultimate strength of the material at the appropriate temperature plays the role of the ultimate stress, is used. To take into account the accumulation of damage during creep and determine the criterion before failure, scalar and vector damage parameters are used, while the components of the vector damage parameter are related to the space of principal stresses. To estimate the rate of the diffusion process, an approximate method for solving the diffusion equation is used, based on the introduction of a diffusion front. Taking into account the influence of the medium on the time to failure is carried out by introducing a function of the integral average concentration into the constitutive and kinetic linear fractional relations. A comparison of time to fracture using scalar and vector damage parameters has been carried out. The features of using a linear fractional model to describe processes of long-term destruction are determined.</p>