We investigated Raman gain spectrum and its dependence on Stoke's shift for fiber Raman amplifiers (FRAs). We determined that the Raman gain spectrum is fairly broad with a gain variation of less than 1 dB from the pump wavelength of 1440 to 1460 nm with maximum gain at 1451.2 nm, which corresponds to a Stoke's shift of 13.4 THz for the input signal source at 1550 nm. Also, the effect of both a co-propagating and counter-propagating scheme on FRAs was studied without using any booster before the Raman fiber, and it was determined that a small signal gain in the case of the counter-propagating scheme is much higher than that of the co-propagating scheme. The impact of the Raman constant (fr) on gain saturation is also illustrated. We have demonstrated that at high fr (<0.18), gain saturation conditions worsen. This suggests that higher saturation input powers can be achieved by selecting an fr value of 0.18 for small-signal gains of 20 dB and an input power of −20 dBm. We have numerically simulated the gain of a FRA for different Raman fiber lengths using varying pump powers. Gain saturation was observed when the input powers exceeded 5 dBm in an amplifier with a small signal gain of 20 dB, pump power of 1.2 W, and Raman fiber length of 8 km.