Abstract: The basic differentia] equations of the conical thin shells are derived by the variational principle. The deformations of the element in the middle surface of the shell and its rotation about all axes are considered in the derivation of these equations. Finally, they are deduced to three differential equations in terms of the displacements, which can be applied to any loaded case without the restraints of the "Donnell-type" equations and the illusions in establishment of the differential equations of conical shells based on the pure physical intuitions.As an numerical example, a buckling problem of a complete cone under external pressure is solved by the Galerkin's method and a simple formula for the critical pressure is obtained. The results are in good agreement w ith the experimental data.