The finite element method (FEM) was carried out to investigate the eigenmodes of square hole-assisted photonic crystal fiber (HAPCF). The Krylov-Schur iteration method was applied to solve the large matrix eigen equation that resulted from FEM. HAPCF is conventional optical fiber with air holes added on the interface between the core and cladding. HAPCF is divided into two classes. One has a buffer coated with a perfect conductor and the other was constructed with the same buffer of the dielectric as the cladding. As a result, transverse magnetic (TM) and transverse electric (TE) spectra were described schematically with the transverse vector fields, the longitudinal scalar fields and their projected contour lines on the cross section of the fiber. The mode types could be determined mainly with the contour lines of the longitudinal scalar field on the cross section of HAPCF. It was found that the buffer coated with the perfect conductor has a great influence on the forming characteristics of the eigenmodes. From the spectra, it was identified that the TM transverse vector fields were almost perfectly constrained in the core area, but the transverse vector fields of TE modes were distributed over to the buffer layer. So, it was understood that more reliable analysis is possible when describing eigenmodes with these three kinds of spectra.