ASME Code VIII-2-2019 and previous versions provided three screening criteria for fatigue analysis. From edition 2004 to 2019, the design factor for material allowable stress decreased and the considered range of permissible cyclic number for design fatigue curve extended. However, screening criteria are almost unchanged except one restriction: If the specified number of cycles is greater than 106, then the screening criteria are not applicable and a fatigue analysis is required. In this paper, percentage limit of the design pressure in method A is modified and the specified number of cycles is extended. Some revision suggestions are also proposed to broaden the applicable range of the screening criterion.