Abstract: At present, an important subject on the shakedown analysis is to study the strategies of applications, search for efficient and feasible computational methods so that the shakedown theory can find its applications in engineering practice. This paper firstly summarizes the current research situations of the structural shakedown analysis numerical methods, and analyzes the current research situations for the shakedown analysis of pressure vessels with volume defects at home and abroad. It will have a certain guiding effect for the further shakedown analysis of pressure vessels with volume defects from now on.