Physical model was established to describe the broadband pulsed laser amplification processes. In this model, Cross relaxation was introduced to study the transformation of homogeneous and inhomogeneous population inversion after laser passage. Hybrid-widened linewidth, homogeneity and inhomogeneity were emphatically considered, which were had not been take into account in other models. Based on the physical model, computer simulation software CPAP for broadband pulse laser amplification process was developed. At last, we discussed the possibility that this broadband physical model can be transfered to the narrow_band physical model under certain conditions.