In this paper we are modeling the interplay of material and form birefringence in photonic crystal fibers. We introduce an efficient numerical method for the calculation of the modal structure. Our approach relies solving the fully vectorial wave equation for the transverse magnetic field and the respective propagation constants using a plane wave expansion. The method accounts for a simple form of material anisotropy. Our analysis is relevant to certain applications areas, and in particular to fiber sensing, where material birefringence arises for instance due to transversally apllied mechanical stress. We analyze the influence of material birefringence and the state of polarization of the fundamental mode.