For the realization of multi-mode optical fiber based long haul transmission systems with space division multiplexing, new erbium doped amplifiers have to be developed. Accurate amplifier simulation models are indispensable tools for this development task. We investigate the impact of mode beating effects on amplifier characteristics. The impact of mode beating is caused by the nonlinear dependence of the population densities on the power densities. Gain and noise figure values, calculated taking the impact of pump mode beating on population inversion into account, are compared with values where interference has been neglected and only power addition has been used. We compare results calculated with the exact waveguide modes with results obtained using linearly polarized modes for pumping and find that occurring beat lengths between fiber modes of one mode group have a noticeable impact on the amplifier performance. We study this effect by investigating how this impacts population inversion along the doped fiber of the amplifier.