The authors have developed a finite element analysis (FEA) program based on an explicit method, including a modified incremental technique. Moreover, it has been modified to consider the elasto-plastic (EP) behavior of refractories in the compression stress-strain curve. Firstly, this paper verifies its validity through EP analysis of the steel beam with similar mechanical properties to the bottom steel plate of the composite beam. Secondly, we show the results of FE analysis by considering the materially non-linearity of the composite beam. Finally, we indicate that the effect of finite element division and incremental displacement size on the inelastic analysis results of the composite beam consisted of refractory and steel plate subject to bending load.