This paper proposes a theoretical method using finite element analysis (FEA) to calculate the plastic collapse loads of pressure vessels under internal pressure, and compares the analytical methods according to three criteria stated in the ASME Boiler Pressure Vessel Code. First, a finite element technique using the arc-length algorithm and the restart analysis is developed to conduct the plastic collapse analysis of vessels, which includes the material and geometry non-linear properties of vessels. Second,as the mechanical properties of vessels are assumed to be elastic-perfectly plastic, the limit load analysis is performed by employing the Newton-Raphson algorithm, while the limit pressure of vessels is obtained by the twice-elastic-slope method and the tangent intersection method respectively to avoid excessive deformation. Finally, the elastic stress analysis under working pressure is conducted and the stress strength of vessels is checked by sorting the stress results. The results are compared with those obtained by experiments and other existing models. This work provides a reference for the selection of the failure criteria and the calculation of the plastic collapse load.