Partitioning and transmutation of minor actinides are expected to have a positive impact on the future of nuclear technology. Their deployment would lead to incineration of hazardous nuclides and could potentially provide additional fuel supply. The U.S. DOE NERI Project assesses the possibility, advantages and limitations of involving minor actinides as a fuel component. The analysis takes into consideration and compares capabilities of actiniae-fueled VHTRs with pebble-bed and prismatic cores to approach a reactor lifetime long operation without intermediate refueling. A hybrid Monte Carlo-deterministic methodology has been adopted for coupled neutronics-thermal hydraulics design studies of VHTRs. Within the computational scheme, the key technical issues are being addressed and resolved by implementing efficient automated modeling procedures and sequences, combining Monte Carlo and deterministic approaches, developing and applying realistic 3D coupled neutronics-thermal-hydraulics models with multi-heterogeneity treatments, developing and performing experimental/ computational benchmarks for model verification and validation, analyzing uncertainty effects and error propagation. This paper introduces the suggested modeling approach, discusses benchmark results and the preliminary analysis of actinide-fueled VHTRs. The presented up-to-date results are in agreement with the available experimental data. Studies of VHTRs with minor actinides suggest promising performance.