Abstract: This paper is concerned with high-order approximation of thick-walled cylinders.Stress expressions are selected to satisfy the three-dimensional axisymmetric stress equilibrium equations and stress boundary conditions at the surfaces of the cylinders. Variation and integration of the stress expressions are conducted and the Euler equations and corresponding end conditions are established. To verify the present Kantorovich-type approximation, an example is provided andcomparison is made with the theoretical solution. It is shown that the present solution is more accurate than the first-order approximation.