Abstract: In this paper, the conjugate second-order deflectiondifferential equation is derived for the global shell axial symmetricalbending problem, and the solution in elementary functions is obtained.Shell of revolution is one of the three basic shells in thin shell theoryand the global shell differential equation is a typical equation for shell ofrevolution. The conjugate second-order deflection differential equation is notonly the simplest global shell differential equation but also the deflectiondifferential equation most commonly used. Differential equationof deflections can satisfy the boundary conditions simply, whichsimplifies the calculation.