Abstract: This paper is concerned with the toraional stability analysis of circular conical shells under circumferential tangential loads.The exact buckling bifurcation equations for the circular conical shells are studied By choosing the buckling modes close to the bifurcation point and the use of Galerkin method the characteristic equations are derived. The critical buckling shear is computed for shells in any conicity . Both hinged and clamped end conditions are considered in the analysis.