Abstract: The purpose of this paper is to improve some of techniques in designing a piston cylinder,ultra-high pressure vessel.First it introduces the elastoplastic analysis of the twofold cylinder which has been autofretted after shrink on and presents the formulae of autofrettage pressure and its characteristic values. Then it derives the formulae of stress distribution in different regions and the formulae of displacements and strains in the yield region. In addition it proposes the approximate calculation methods of fracture analyses.Based on the results,the strength and fracture analyses have been made for the vessel. In analysing,two cases have been considered: autofrettage after shrink on and shrink on after autofrettage. Adopted are: 1) the material used is perfectly elastoplastic and 2) the axial stress is independent of the coordinate,r.