Abstract: The analytical solutions for the limit analysis of pressure vessels and pipelines with volumetrical defects are very difficult to find because of the complexities of their structures and load conditions. So, people put the research emphasis upon the feasible and efficient numerical methods. The paper summarizes the current research situations for the structural limit analysis numerical methods and emphatically analyzes the current research situations for the limit analysis of pressure vessels and pipelines with volumetrical defects at home and abroad. The research results will be important and useful for guiding the limit analysis of pressure vessels and pipelines with volumetrical defects.