In this paper we will study the effects of the Stimulated Brillouin Scattering (SBS) in Distributed Erbium Doped Fiber Amplifiers (DEDFAs). A model for predicting gain of the DEDFAs that affected by SBS will be introduced. The results of modeling and simulation have shown that the SBS will cause backward scattering of the pump light and causes a reduction in the gain of DEDFAs and this gain reduction depends on the pump laser linewidth. The Numerical results show that there is a threshold value for this gain reduction. The threshold value of laser linewidth for minimizing the gain reduction due to SBS will be obtained.