This paper presents results for the method of characteristics solver of the neutron transport equation, MOCFE, incorporated in the UNlC code. The main difference with respect to other MOC based codes is the use of a finite element mesh rather than a combinatorial geometry. The details on the impacts this has on ray tracing are described and the efficiency of the approach is discussed. The MOCFE currently treats linear and quadratic triangular and quadrilateral finite elements in two-dimensions and linear tetrahedrons and quadratic hexahedrons in three-dimensions. Benchmark results for the fourth Takeda benchmark and the two-dimensional component of the OECD C5G7 benchmark are discussed. The details of the early parallel aspects of the code are discussed along with our plans for future development.