Calculations have been conducted for the KRITZ-2 (KRITZ-LWR-RESR-001/002/003) and the Fast Flux Test Facility (FFTF) (FFTF-LMFR-RESR-001) Nuclear Energy Agency benchmark problems using the PARCS reactor simulation code with lattice parameters generated by the DRAGON reactor physics code and with the MCNP6 Monte Carlo code. The benchmark analyses examined the DRAGON cross-section library, PARCS energy group structure, DRAGON fuel assembly modeling, and nuclide self-shielding effect. For KRITZ-2, the PARCS 2-group core calculations with a DRAGON 361-group library based on ENDF/B-VII.1 reproduced the benchmark keff with a root-mean-square (rms) error of 0.19% δk. DRAGON/PARCS also predicted the fission rates within 5%. The MCNP results are consistent with the DRAGON/PARCS results but with a small underestimation when compared to the benchmark value. For FFTF, the PARCS 33-group core calculations underpredicted the benchmark keff by 0.19% δk while the MCNP calculation overpredicted the benchmark keff by 0.23% δk. The neutron spectrum distributions calculated by PARCS and MCNP are consistent with measured data. Since the energy boundary values of the measured neutron spectrum are not available, the calculated spectra could not be directly compared to the measured value. The DRAGON/PARCS solution to a numerical benchmark of a gas-cooled fast reactor (GFR), i.e., the Energy Multiplier Module, predicted the keff and assembly power with 0.46% δk and 3.7% rms error, respectively, when compared to the MCNP simulation. The benchmark calculations of the selected thermal and fast reactors have shown that DRAGON/PARCS simulates small reactor cores with good accuracy.