This paper provides results for calculations performed using MCNP6’s unstructured mesh (UM) capabilities based on the three problems described in the Kobayashi benchmark suite. These calculations are performed to provide a comprehensive and consistent basis for the verification and validation of MCNP6’s constructive solid geometry (CSG) and UM neutron transport capabilities relative to a well-known analytic benchmark. First, preexisting MCNP5 CSG models are updated and reexecuted to form a basis of comparison with UM for both the consistency of the numeric results and speed of execution. Next, a series of UM calculations is performed using first- and second-order tetrahedral and hexahedral elements with mesh generated using Abaqus. In addition, a different first-order tetrahedral mesh is generated with Attila4MC in order to investigate the effect on the results. When executed, the results for both CSG and UM agree among themselves and with the benchmark quantities within reasonable statistical fluctuations (at worst, the results agree within 2σ or 10% but generally within 1σ or 5%) and recognizing from historical work that improved agreement is possible with additional variance-reduction effort. As expected, for the simple geometries herein, we find the CSG calculations completing approximately ten times faster than the comparable fastest UM calculations. We find minor speed differences (~1%) between multigroup and continuous-energy nuclear data and significant speed differences (factor ~100) between different element types. As such, the timing results support the recommendation that users run with the simplest UM element type that adequately represents the problem geometry, ideally first-order hexahedra, and with the most convenient nuclear data energy treatment.