This paper presents a modeling of a synchronous machine infinite bus system of which not only seperated saturation effect but also cross magnetization effect of the saturated generator is included for the more precise analysis of the system. In the process of reforming the flux linkage equations of the state equations which have generator saturation effects, the d-axis coordinated system of a generator is fixed that the d-axis proceeds the q-axis in $90^{circ}$ to accord with the generally accepted generator model used before. The simulation results show that cross magnetization has a very important effect to the more precise eigenvalue analysis of steady state stability.bility.