Abstract: In the present paper, we give the thickness formulation of thin conical shallowshell with variable thickness h=h₀1+β(r/a)^γ,(γ>0). By using the modified iterationmethod for solving the problem of nonlinear stability of thin conical shallow shells with variable thickness subjected to uniformly loads under the calmped edges is solved, more accurate second order approximate analytical solution is obtained. The numerical results have been given in figures and tabular forms.