The article is devoted to computer modeling of the process of possible damage to the pipelines of nuclear power plants that received local thinning of the walls.The geometric features of pipelines are essential not only for assessing the intensity of erosion and corrosion of a metal, but also for the final strength assessment, in particular, when calculating local thinning of the walls of pipelines. The accuracy of forecasts of the life of pipeline structures directly depends on the ability to evaluate the strength of pipeline elements that have received local thinning, especially if these elements themselves have a complex shape. Such elements include elbows, nozzles, adapters (transitions), shells. All of these elements are thin-walled structures of complex shape. Computer modeling of the process of crack formation and growth requires solving several problems. A review and critical analysis of the available experimental information on the growth rates of cracks in specific structural materials and in the environment that is characteristic of given operating conditions is required. An assessment of the crack growth rate is impossible without determining the stresses and strains in the shell structure of complex spatial geometry. The development of routine criteria for crack growth and their attachment to a stress-strain state calculation program is the next task. To solve these problems, a complex of three-dimensional finite element methodologies and programs based on the theory of thick shells has been created. The article presents some results of calculating the stress-strain state of adapters and the growth of cracks in them.