This paper discusses the strength design methods in ASME Boiler and Pressure Vessel (B&PV)Code with a focus on the design by analysis for engineering design and integrity assessment of pressure vessels and the innovative technology and development made recently towards plastic flow criteria for improving the pressure vessel design and assessment methods.The pressure vessels are of high pressure and include nuclear plant pressure vessels, petrochemical pressure vessels, storage tanks and oil/gas line pipes.This work presents (1) a simple review of the traditional strength criteria used in ASME B&PV Code and in industry, (2) shortcomings of the existing strength criteria when used in prediction of burst pressure of cylindrical vessels, (3) advantages of plastic flow theories used for pressure vessel analysis,(4) challenges, technical gaps and needs to improve the traditional strength criteria, (5) existing flow criteria and their shortcomings in prediction of burst pressure of cylindrical vessels, (6) a new multi-axial flow theory and its burst pressure model for cylindrical vessels, (7) experimental validation of the new flow criterion by use of full-scale experimental data for carbon steels, (8) applications of the new flow criterion, and (9) recommendations for further investigation of structural design and assessment methods.