The characteristic of fault arc ignited between two metal rod electrodes in a closed air container with AC current has been investigated in magneto-hydrodynamic (MHD) method. Based on a set of governing equations in coupled electromagnetic and gas dynamic fields, a three-dimensional (3D) air arc model is constructed and solved, which predicts the distributions of temperature and pressure of arc plasma with the temperature, flow, electromagnetic, turbulence and radiation field taken into account. Particularly the internal pressure development at different locations in the container are calculated and compared. Besides, the fraction of electric arc energy leading to pressure rise, which is known as kp factor and calculated according to measured experimental results before, is determined by using the numerical method alone without any experimental data supporting. The effect of different radiation models on pressure rise is analyzed and compared. The result shows that the semi-empirical radiation model is more suitable to the pressure calculation in comparison to the net emission coefficients(NEC) model. The simulation results of the pressure rise, kp, arc voltage and arc power agree with the experiments.