Erbium-Doped Fiber Amplifiers (EDFA) are one of the most widely used optical amplifiers in the field of optical communications and fiber lasers. Theoretical models based on the rate equations, therefore, were developed to predict the performance of such amplifiers. The goal of this thesis is to provide a numerical model for EDFAs and verify its validity through experimental measurements. Two computer programs based on two different numerical methods (the Finite Difference method and the 4th Order Runge-Kutta Method) to solve differential equations were written. The different fiber parameters to build the model including absorption and emission cross-sections and scattering losses were experimentally determined. Two different optical amplifiers were built using different lengths of doped Erbium fiber. Experimental output signal optical power and gain of the two amplifiers were measured for different values of input signal power and pump power. These results were predicted by the numerical model with a considerable degree of accuracy.