Abstract: In this paper, the flexural stability analyses of varying thickness conical shells subjected to uniform external pressure using perturbational method is described, and the apparent expressions of buckling loads for variable thickness functions is derivecl. Besides above these, It is also proved that, although the equations of stability theory simplified by 2 is the same only as ones of zero order perturbational approximation, the expression of buckling loads given in 2 is accurate to the first order of appoximation in the case of constant thickness.