The large axially symmetric deflections of a thin elastic shell of revolution under the axial force applied to the shell edges has been studied. The equation of equilibrium and the relations of elasticity have been used for finding the shell strain. This problem is very sensitive to the type of the initial equations. As an example the conic shell has been examined. The generalized formula for finding the axial force has been obtained. The comparison of the results of using the various modifications of the initial equations of the shell theory has been represented.