Acta Scientiarum Polonorum

In the present paper, an infinite system of homogeneous differential equations in the Cauchy normal form
was obtained to solve the problem of the stability of cylindrical anisotropic layered shells under the action of
external torque, based on the spatial relationship of elasticity theory. The components of the stress state that
are necessary to solve the equation system were derived analytically by using the generalised Hooke’s law.
The results are obtained for a single-layer cylinder, and compared with the values of critical loads calculated
using the well-known method proposed by Lechnitsky. The suggested approach could be implemented, for
instance, to solve the problem of cylindrical two-layer shell stability under the action of torque, which is
projected by calculating the shear stress.