This invention deals with multi-component composite materials and techniques for improved shielding of neutron and gamma radiation emitting from transuranic, high-level and low-level radioactive wastes. Selective naturally occurring mineral materials are utilized to formulate, in various proportions, multi-component composite materials. Such materials are enriched with atoms that provide a substantial cumulative absorptive capacity to absorb or shield neutron and gamma radiation of variable fluxes and energies. The use of naturally occurring minerals in synergistic combination with formulated modified cement grout matrix, polymer modified asphaltene and maltene grout matrix, and polymer modified polyurethane foam grout matrix provide the radiation shielding product. These grout matrices are used as carriers for the radiation shielding composite materials and offer desired engineering and thermal attributes for various radiation management applications.