Numerical solution for the surge and rotating stall in axial flow compressor is considered. The main objective of this study is to explain the unsteady behavior of the rotating stall and surge phenomena to increase the value of stability for the axial compressor. The performance of the compressor will be improved significantly by decreasing the effect of stall and surge for axial flow compressor. The results are verified as compared with wellknown published experimental results, the results are found to be in an excellent agreement. Effect of main dimensionless parameters such as compressor length/compressor diameter and flow velocity are considered. It is found that the increasing the velocity parameter up to two the surge will change from classical surge into the deep surge. Also, the increase of the compressor dimensionless length up to 8 will cause the surge and rotating stall to reach the stable condition faster than the cause when it is equal to 4. Also, it is important to notice that Fehlbergmethod predicted the surge and rotating stall much closer to the Runge Kutta fourth degree method by about 7%.