Using parameters of Nd∶glass and Ti∶sapphire, simulation to nonlinear SchrAo¨Gdinger equation about chirped pulse propagation was demonstrated by split step Fourier method, the effect of self phase modulation, gain narrowing and gain saturation to amplified chirped pulses was discussed, and distorted intensity profiles of amplified pulses were also demonstrated here. Putting emphasis on the effect of self phase modulation and inter relationship between self phase and other two nonlinear effects, the analysis presented here is valid for high power laser amplifier designing.