In the paper the results of the analysis of propagation of the low-frequency electromagnetic waves across the multilayer cylindrical shell are presented. The mathematical model of non-local bilateral boundary conditions of multilayer cylindrical shells was created. These non-local bilateral boundary conditions describe the penetration of low-frequency electromagnetic waves across layers of the shell. The method of transformation of the boundary problem to the integral Fredholm equations of the second kind was developed. Furthermore, the value of efficiency coefficient of the shell was calculated. Analytical transformations are based on the Bessel functions.