Abstract: In this paper, after taking power functions as trial functions nonlirear stability of a shallow conical thin shell under axisymmetrical distributed load si solved by the Moment Method. Elastic edges are consi deredo Rigidly clamped, clamped but free to slip, simply hinged and sire ply supported edges are dealt as its four special cases. Distributed loadis regarded as polynomial function or uniformly distributed moment alhing the edge. Under uniform distributed load with clamped edger resultso obtained by MM are compared with those obtained by perturtation Method. In the paper, characteristics of PM and Method of Weighted residua ls are discussed and it is much easier to write general computer programs by MWR.