Abstract: Paying attention to the event of damage of the cylinder of eccentric hydraulic piston pump, the author gave a comment on application of geometric mean treatment method in calculation of elastic loss of stability of thick circular pipe of non-uniform wall thickness and demonstrated thrcugh the calculation of critical pressure of elastic loss of press bar with altered sections that the method results in a evident error and collapse of cylinder of eccentric pump takes place in the external elastic range. An analysis on technical background of the tests carried by Soviet scientist Yeneminko, theory of linear elasticity of minor bending deflection, choice of deformation curve of thin circular pipe with non-uniform wall thickness and a set of factors that affect accuracy of approximate solutions was described in the paper.The author pointed out that there is a necessity to search theoretically different approximate solutions of elastic loss of stability of circular pipe with non-uniform wall thickness and to carry tests upon elastic loss of stability of circular pipe of non-uniform wall thickness caused by eccentricity of external and internal circles.