By analyzing several types of waveguide structures, we demonstrate that a polarization-insensitive semiconductor optical amplifier can be designed by using an anisotropic gain medium or a properly shaped active region. In particular, we calculate the waveguide parameters required for achieving polarization-insensitive optical amplification and discuss their tolerances. Our results show that considerable flexibility in the design of polarization-insensitive amplifiers can be offered by tailoring the waveguide structures of the amplifiers.