A comprehensive observation of the stimulated Brillouin scattering (SBS) phenomena in a high power nanosecond linearly polarized Yb-doped double-clad fiber amplifier is presented. According to the behavior of SBS, the amplification process is divided into four regions. All the temporal, spectral and power characteristics of SBS in both forward and backward directions in each region are described in detail. Cascaded SBS with up to 30 orders of Stokes waves and 10 orders of anti-Stokes waves is observed. The fiber damage caused by the giant SBS pulses is reported. And the influence of the linewidth, pulse duration, feedback and polarization on SBS is discussed.