The present invention is a shielding material that resists both nuclear radiation and high temperatures and is especially suited to encasing radioactive waster materials to immobilize them. The material is a mixture comprised of two or more organic polymers in which included fillers are cross-linked within the phenylic side chains of the polymers and copolymers. Other fillers provide radioactive shielding and may be merely included within the cross-linked matrix. The material contains a tough matrix with embedded particles of radiation shielding substances and thermoconductive materials with an overall ceramic-like or ceramometallic properties. The material is thermosetting and can present an extremely hard material -e.g., 20,000 p.s.i. shear strength. The material is comprised of a mixture of vulcanized rubber and/or rubber-like polymers, various radiation shielding inclusions, polyimide resin and phenolformaldehyde resin. After being mixed in the proper proportions the material sets up at an elevated temperature (e.g., 260 °C). The final material has a density of between 8 and 50 pounds per cubic foot depending on the proportion and identity of the radiation resistant inclusions.