The axial polarization pulling, due to stimulated Brillouin scattering (SBS) in linear polarization maintaining fibers (PMFs), is proposed, simulated by vectored SBS equations, and demonstrated experimentally. The simulation shows that the SBS pulling is always towards one of principal axes of PMF, depending on the pump light projection of the input state of polarization (SOP) on the polarization vector of PMFs. Based on this principle, an SBS fiber laser with 20 in PMF is configured. Further, we observe that the SOP of lasing light switches between two orthogonal SOPs, as the pump light changes its SOP between two half spheres of the Poincare sphere. Moreover, the orthogonal polarization switching (OPS) scenarios relating to different powers and SOPs of pump light are studied. We analyze and experimentally demonstrate the lasing conditions for the fully polarized OPS state, where only one of the principal polarization modes resonates, as well as the depolarization state, where two principal polarization modes resonate simultaneously. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement