This study employs thermal and epithermal neutron activation analysis (NAA) to quantitatively and specifically determine absorption dose rates to various body parts from uranium, thorium and potassium. Specifically, a case study of bauxite residue (red mud) from an industrial facility was used to demonstrate the feasibility of the NAA approach for radiological safety assessment, using small sample sizes to ascertain the activities of U, U, Th and K. This proof-of-concept was shown to produce reliable results and a similar approach could be used for quantitative assessment of other samples with possible radiological significance. U and Th were determined by epithermal and thermal neutron activation analysis, respectively. U was determined based on the known isotopic ratio of U/ U. K was also determined using epithermal neutron activation analysis to measure total potassium content and then subtracting its isotopic contribution. Furthermore, the work demonstrates the application of Monte Carlo Neutral-Particle (MCNP) simulations to estimate the radiation dose from large quantities of red mud, to assure the safety of humans and the surrounding environment. Phantoms were employed to observe the dose distribution throughout the human body demonstrating radiation effects on each individual organ.