Sealing analysis of sealing system in reactor pressure vessels is relevant with multiple nonlinear coupled-field effects, so even large-scale commercial finite element software cannot finish the complicated analysis. A fmite element method of 3D transient coupled thermo-elastic-plastic contact sealing analysis for reactor pressure vessels is presented, in which the surface nonlinearity,material nonlinearity, transient heat transfer nonlinearity and multiple coupled effect are taken into account and the sealing equation is coupling solved in iterative procedure. At the same time, a computational analysis program is developed, which is applied in the sealing analysis of experimental reactor pressure vessel, and the numerical results are in good coincidence with the experimental results. This program is also successful in analyzing the practical problem in engineering.