The beam propagation method (BPM) is one of the most powerful numerical technique for analyzing fibers and integrated optics devices. Recently, a vectorial formulation scheme based on finite element method for isotropic medium was developed. The magnetic field is adopted instead of the electric one. A new method, although based on nodal finite elements, was developed to solve instead the vectorial wave equation in terms of the transverse components, reducing computational efforts and resources by roughly 50%. The new method is extended to analyze anisotropic medium with off-diagonal elements in the permittivity tensor due to optical axis misalignment induced by elasto-optics effect.