In this study, we show that transformation optics formalism can be used to rigorously model a wide range of twisted anisotropic fibers, which could only be analyzed using perturbative methods. If the material anisotropy of fibers has an intrinsic origin or is induced by axially or helically symmetric physical factors, then they can be transformed into a form usable in rigorous two-dimensional (2D) modeling. We demonstrate the effectiveness of the proposed approach in 2D modeling of the propagation characteristics of first-order eigenmodes in twisted and spun fibers with high linear birefringence. We derive the equivalent electric permittivity tensors for such fibers in the helical coordinate system and study the evolution of the first-order modes toward vortex modes with increasing twist rate. The obtained results confirm that the proposed method can reveal phenomena that cannot be predicted by analytical approaches.