Cement-based concretes are commonly used for managing radioactive waste due to their low cost and radiation shielding properties. However, the potential of using oil shale ash as an additive in waste packaging material has been overlooked. This study focuses on benchmarking and developing a Monte Carlo based modeling methodology using multiple transport codes (MCNP, SERPENT, SCALE, OpenMC, and EGSnrc) to assess the effects of these additives on the gamma and neutron shielding properties of concrete. The cross-code comparison showed that all transport codes are in excellent agreement with each other. Investigations into oil shale ash demonstrated similar properties to fly ash. The addition of oil shale ash had a negligible effect on low-level waste (LLW) gamma shielding properties and a minor negative effect on neutron shielding properties. The addition of basalt-boron fibers indicated a minor negative effect on LLW gamma shielding properties but a significant positive effect on neutron shielding properties. The presence of basalt-boron fibers considerably decreased the photon flux resulting from the activation of concrete. In conclusion, this study offers valuable insights into utilizing radiation transport codes to analyze the interactions between radiation particles and innovative concrete additives.