An analytical model for estimating the stress -induced birefringence in true Panda-type polarization -maintaining fibers with imperfect geometry has been developed in this letter. The developed model is simpler and more accurate compared to conventional sophisticated and asymptotic formulas in reported works. Our model provides a clear and simple solution to demonstrate the periodic dependence of the birefringence on the misalignment angle between the two stress-applying parts, and the monotonic dependence on the geometric parameters of stress-applying parts. Our work also reveals the important role of the misalignment angle between the two stress-applying parts in practical Panda-type fibers.