The constructed finite element stiffness matrix of a flexible beam based on Winkler. Within the item to the desired function beam deflection applied not approximate approximation and using an exact solution of the differential equation of the problem, defined functions Krylov. Examples demonstrate the effectiveness of the developed element. An analogy between the differential equations of the bending beam under Winkler and the differential equation of equilibrium of a flexible cylindrical shell under axisymmetric loading. Study the behavior of displacements and forces in the shell. We show by example the phenomenon of edge effect, built on the basis of functions Krylov.