Limit analysis can explore the bearing potential of materials and structures, and is widely used in structural optimization and safety assessment of pressure equipment. This paper introduces the limit analysis and application of pressure vessel components, straight sections of pressure pipelines and pipe fittings for the purpose of preventing quasi-static loading strength failure since the Eighth Five Year Plan. In addition, recent studies on the characterization of the metal material's constitutive relations after necking phenomenon and the application of the local strain failure criterion based on the true stress–strain extrapolation curve after diameter shrinkage to smooth specimens, notched specimens and large-diameter thin-walled full-size tube section specimens are also described. Finally, some suggestions for further research are put forward.