Light polarization characteristics of the near-band-edge optical transitions in m-plane AlxGa1-xN epilayers suffering from anisotropic stresses are quantitatively explained. The epilayers were grown on an m-plane freestanding GaN substrate by both ammonia-source molecular beam epitaxy and metalorganic vapor phase epitaxy methods. The light polarization direction altered from E⟂c to E//c at the AlN mole fraction, x, between 0.25 and 0.32, where E is the electric field component of the light and ⟂ and//represent perpendicular and parallel, respectively. To give a quantitative explanation for the result, energies and oscillator strengths of the exciton transitions involving three separate valence bands are calculated as functions of strains using the Bir-Pikus Hamiltonian. The calculation predicts that the lowest energy transition (E1) is polarized to the m-axis normal to the surface (X3) for 0< x ≤T1, meaning that E1 emission is principally undetectable from the surface normal for any in-plane tensile strained AlxGa1-xN. The polarization direction of observable surface emission is predicted to alter from c-axis normal (X1) to c-axis parallel (X2) for the middle energy transition (E2) and X2 to X1 for the highest energy transition (E3) between x = 0.25 and 0.32. The experimental results are consistently reproduced by the calculation.