This dissertation develops a model for numerical analysis of stimulated Brillouin scattering (SBS) effects and the development of suppression techniques for the realization of increased output power levels for high power ytterbium-doped dual clad fiber amplifiers. The overall objective of this effort is to develop and validate a predictive model to assist in the determination of the most effective techniques for increasing SBS thresholds within ytterbium-doped fiber amplifiers in order to realize increased power output. The goal is to demonstrate an increase in SBS threshold that would increase the output power potential in ytterbium-doped fiber amplifiers by at least an order of magnitude. The approach determines the effect of changing the acoustic properties of fiber cores on the Brillouin frequencies and the effects of various signal modulation schemes on active ytterbium-doped fiber amplifiers. In addition, temperature effects and temperature differentials within the fibers are predicted and measured, both with passive and active fibers. Brillouin center frequency responses of various germanium dopant concentrations within the cores, as well as the effects of fiber segment combinations are measured in the lab. The effects of various phase modulation schemes of the signal are predicted and measured for passive fibers. Results from these measurements are used to validate and adjust the model accordingly. Finally, the manufacturability of relevant characteristics required to achieve such SBS suppression is evaluated, identifying constraints and limitations for utilization of low cost fabrication techniques. The final model, validated and adjusted with empirical results, supports the suppression of SBS in standard ytterbium-doped fiber amplifiers by over a decade.