The variant of the classical theory of shells (CTS) built on the basis of Lagrange analytical me- chanics is under analysis. The direct approach to shells as material surfaces, the elements of which are material normals with five degrees of freedom - three translations and two rotations, is used. The sys- tem of equations and boundary conditions is derived from the principle of virtual work with direct tensor calculus. Such approach makes it possible to discard the problems and controversies characteristic of conventional concepts. This paper is aimed at comparing this theory of shells (CTS) with widely known variants, as well as with the solution of the spatial problem.Problems for the thin-walled infinite cylinder have been formulated and solved on the basis of three theories: CTS, the well-known theory of A.L. Goldenweiser and three-dimensional elasticity the- ory. For the shell-based models, we have linear algebraic systems, for the three-dimensional models - the ordinary differential equation (ODE) over the thickness. Exponential solutions of static problems with different variability are built analytically. Numerical solutions using computer mathematics have been found.In comparing exponents of solutions with the boundary load, it was found that for small values of the wave number and the shell thickness, both shell theories agree well with the three-dimensional the- ory. As the wavelength decreases relative to the shell thickness, their uncertainty increases, though the area of CTS applicability has turned to be somewhat wider than that in the theory of A.L. Goldenweiser.According to both theories, the detected displacements of the shell under the load rapidly changing by the coordinates are well coordinated with each other. The coordination with the three- dimensional theory is suitable for small values of wave numbers. The calculations have shown that, under external load having the axial and circumferential components, CTS predicts a normal displace- ment component with a greater accuracy.

elastic shell, Lagrange mechanics, thin-walled cylinder, theory of elasticity, statics, rapidly changing load.