We report on an experimental analysis of stimulated Brillouin scattering (SBS) in a 20-m-long highly birefringent microstructure fiber for sensing applications. In particular, an experimental setup based on Brillouin optical frequency-domain analysis, operating at a wavelength of 1550 nm, has been employed in order to analyze the distribution of Brillouin frequency shift along the fiber, as well as to study the dependence of Brillouin frequency shift on optical polarization, temperature, and strain. Our results indicate that, for any fixed polarization, the fiber has a dual-peaked Brillouin spectrum. A study about the origin of these two peaks is presented.