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A numerical model is developed to simulate stimulated Brillouin scattering (SBS) in high power single-mode fiber amplifiers. The time dependent model incorporates both laser and Stokes wave amplification and initiates the Brillouin scattering from thermal phonons. A frequency chirped laser is used as the seed to suppress SBS. Experiments with Yb-doped fiber amplifiers show good agreement with the modeling. Using experimentally determined parameters, the model is used to predict chirp requirements for multi-kilowatt amplifiers with tens of meters of delivery fiber. A comparison is made between a chirped seed source and random phase modulation for SBS suppression.