We present an analytical theory based on a steady-state rate equations that describe pump power, stimulated Brillouin scattering (SBS) power, amplified spontaneous emission (ASE) and output power of a single-frequency 1018nm short wavelength fiber amplifier. A detailed model that accounts for amplified spontaneous emission (ASE) and stimulated Brillouin scattering (SBS) in relation to the ASE gain, Brillouin gain, fiber length, seed power, the linewidth of seed laser, and available pump power in both co-pumped, counter-pumped and bidirectional configurations is developed. It is found that when fiber length is optimized, the amplifier output power will increase with available pump power. In order to mitigate the SBS process, we can shorten the fiber length or reduce the seed laser power. Although higher output power is obtained with higher seed power, the SBS power will increase, and we find that the same amplifier efficiency is obtained with different pumped configuration, counter-pumped configuration mitigate SBS is more effective than co-pumped configuration and bidirectional configuration. We also calculate the output power and SBS power which consider the linewidth of seed laser by different pumped configuration, we also find that broader linewidth of seed laser can achieve lower SBS output power, but the change of laser power is unobvious with increasing the linewidth of seed laser. In order to suppress the ASE waves, we can shorten the fiber length or increase the seed laser power.