Abstract: The high order FEM (finite element method) was utilized to get the first order eigen-pair and high order eigen-pairs. The performances of the low order FEM and high order FEM were compared and the differences between the uniform nodes and LGL (Legendre-Gauss-Lobatto) nodes were elaborated. The high order FEM was verified to be able to solve the high order eigen-pair accurately in the 2D BIBLIS and 2D IAEA benchmarks. The results show that the high order FEM with the LGL nodes performs faster than the high order FEM with uniform nodes.