Based on coupled-mode theory for linearly polarized (LP) modes, spun dual-lobe stress region fibers (i. e. spun linear birefringence fibers) and spun 4-lobe stress region fibers are theoretically analyzed. The expression of the anisotropic dielectric tensor of the additional stress-induced dielectric constant at the core region of the fiber is presented. By the expression, the coupled-mode equations for the linearly polarized modes propagating in multi-lobe stress region fibers with rotation angle are derived. Then, super-local modes in multi-lobe stress region spun fibers can be obtained by using mode transform. Finally, the fiber birefringence is decided from the phase constants of super-local modes. It is found that high elliptical birefringence can be obtained in spun dual-lobe stress region fibers with ideal symmetry, and there is no birefringence in spun 4-lobe stress region fibers if four lobes are perfectly symmetrical. The same result is valid for spun fibers with 8-lobe and 16-lobe stress region, both of which have zero birefringence.