We investigate the stimulated Brillouin scattering (SBS) and the stimulated Raman scattering (SRS) in an ytterbium-doped double-clad fiber amplifier that outputs optical pulses with multi-ns-duration and multi-hundred-kW peak-power. The ytterbium-doped double-clad fiber amplifier is simulated by a model which is composed of a set of propagation-rate equations. The simulated results show that SBS and SRS will deform the output signal pulse in both the time domain and the spectral domain, and degrade the performance of the ytterbium-doped double-clad fiber amplifier seriously. It is shown in our simulation that the troublesome SBS can be effectively suppressed by broadening the signal linewidth to a critical value of 0.07nm in our calculation, and the effect of SRS can be suppressed using a large-mode-area fiber with proper length. The model and the simulated results are very useful for designing an ultra-high-power ytterbium-doped double-clad fiber amplifier.