Currently fields of optics and photonics have urgent problem of fast and accurate simulation of photonic crystal fibers with different fillings. Although significant progress has been made from the time of first method founding, the rigorous analysis of light propagation remains problematic because of the large index contrast, the vectorial nature of the Maxwell equations and the complicated cross-sections of the hole geometries involved. This paper presents improved fast multipole method for low birefringence materials used in photonic crystal fiber core. Using this method, abruptly growth of modeling speed and accuracy is provided. Previously some research in the field of this method implementation in photonic crystal modeling have carried out, but suitable results for low birefringence fillings have not been reached yet. Implementation of this method for low birefringence fillings on photonic crystals is the main goal of this article. Modeling is implemented in Maple and show next results: monotonic decreasing of refraction index real part and linear character of refractive index imaginary part, attenuation has a plateau in bandwidth range and zero velocity group dispersion at 780 nm. Dissimilarity between numerical results and results presented in datasheet caused by nonideal cylindrical shape of air holes, but not by implemented theoretical method.