According to high strain gradients characteristic at the junction between pressure vessel and nozzle, based on simulating shape plate of pressure vessel nozzle, weak-conforming element models are established for two types of special shape plates, which satisfied weak continuous conditions between elements. The weak-conforming element methods do not need satisfy stress equilibrium conditions. It can solve the conventional finite element difficult to adapt to the singularity of the field. The stresses are obtained by means of weak-conforming element method. The calculation results are in accordance with those of experiment results. This paper provides the foundation for the design of special shape plates and analysis of extending crack.