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Axisymmetric vibrations of thin elastic cylindrical shell under the internal pressure of an incompressible homogeneous ideal fluid flow are analyzed. The mathematical model describing the structure is reduced to a system of ordinary differential linear equations of the second order. Solutions of the problem are obtained by using the approximate theory. The system of equation is solved analytically. The solution contains the unknown constants, which is evaluated by using Mathematika 9.0. Analytical formula for evaluation of components of normal and tangential deflections of the shell middle surface are found. The approximate results are presented by either analytical formulas or in the form of plots. The results are compared with numerical (FEM) results obtained by the program complex ANSYS 13 and agree well.