The paper describes a new method for determining theStress-strain state stress–strain state in layered cylindrical constructions made of isotropic and transversely isotropic materials (the layer “straightening” method), which is a development of the generalized scalarization method for dynamic elastic fields in transversely isotropic media proposed by Sizov (Mechanics of Solids, 5, 55–58 (1988)). The proposed method allows one to obtain an approximate solution to the wave problem in a layer, where obtaining an exact solution by conventional methods is impossible. The use of this method, where the problem conditions allow it, allows one to reduce the time spent on the analytical solution, as well as the computer time in numerical modelingModeling. The “straightening” method can be successfully used in modelingModeling the stress–strain stateStress-strain state in layered cylindrical constructions made of isotropic and transversely isotropic materials, as well as in numerical modeling of the process of diagnosing the state of layered cylindrical structures using the acoustic active method ofNon-destructive testing non-destructive testing.