The thory of RFA with backward Raman pumping and forward Raman pumping is studied by numerical solution combinating interpolation method and Runge-Kutta method. Meanwhile, the most complete characterization and comparison of RFAs with backward Raman pumping or forward Raman pumping for pump power, initial signal power and fiber length is obtained. Through the analysis and comparison, the results show that high-gain amplifier transistor is obtained in backward pumping comparing with forward pumping. Keywords-SRS; FRA; Backward Raman pumping; Forward Raman pumping© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.