Experimental results for the stimulated Brillouin scattering (SBS) in the single-frequency, single-mode, linearly polarized ytterbium-doped fiber amplifier are reported. The fiber amplifier configuration comprises of two-stage master oscillator power amplifier with co-propagating signal and pump light. The evolution of SBS spectra is investigated in the experiments. Multiorder Stokes and anti-Stokes scattering can be observed in the forward and backward directions of the fiber amplifier, which generate through cascaded SBS and four-wave mixing process.