The pressure vessel has great application value in the national economy and it is widely used in petroleum chemical industry, energy industry, scientific research and military industry etc. It will cause accidents of explosion and fire burning which will endanger people's life, property safety and lead to environmental pollution once it is not designed or manufactured in reason，because its working medium usually possessthe characteristics of high temperature , high pressure, and high corrosion, so countries all around the world attach great importance to the design and manufacture of pressure vessel. To overcome blindness exists in the conventional design method and high cost, uncertainties of stress classification method, limit load analysis based on plasticity theory appeared with the rapid development of finite element analysis and the computer technology. Limit load analysis is consistent with elastic―plastic analysis of America standard ASME in ideas of analysis, differs in the numerical model. Elastic―plastic analysis is more in line with the actual situation with higher cost of calculation and analysis. What is more, data of true stress and strain with strain hardening effect of various materials is insufficient. So it is critical to extending the using of limit load analysis.

　　By means of finite element analysis, the plastic limit load of hemispherical head cylindrical shell was researched in this paper.

　　The main contents and achievements weresummarized as follows:

　　(1) The bearing capacity of spherical shell and cylindrical shell are different under the same conditions, and the bearing capacity of spherical shell is relatively larger.

　　(2) The structure of hemispherical head cylindrical shell has three kinds of failure modes under limit load: one is the expansion of cylindrical shell when the hemispherical head has higher bearing capacity; the other is the expansion of hemispherical head when the cylindrical shell has higher bearing capacity; the third is the expansion of hemispherical head with axial tensile of cylindrical shell when the bearing capacity of cylindrical shell equals to that of hemispherical head.

　　(3) The relationship between the limit load and structure parameters was investigated: The limit

　　load will decrease when the radius of cylindrical shell increases; The limit load will increase when the thickness of cylindrical shell increases; The limit load has little change when the length of cylindrical shell increases.

　　(4) The optimum ratio which can make the bearing capacity of cylindrical shell equals to that of hemispherical head was investigated and its effectiveness was verified.

　　(5) The effect of different connectionsbetween cylindrical shell and hemispherical head on limit load was investigated.

　　(6) The engineering estimated formula of cylindrical shell with hemispherical head was fitted

　　and its effectiveness was verified.