The NRS is following the EA’s Guidance on Requirements for Release from Radioactive Substances Regulation.
The site was active between 1959 and 1992 and some of its underground floors and walls have a low level of radioactive contamination.
Some of the waste that will be used to fill the sub-surface structure will also be low-level radioactive waste.
The company said it would not be importing any waste to site from other locations.
It has applied to change its Radioactive Substances Regulations environmental permit, which would give it permission to bury the radioactive materials.
It has also applied for Deposit for Recovery Environmental Permit, which would allow it to bury non-radioactive waste.
Sally Coble, EA nuclear regulation group south manager, said: “We will only vary the radioactive substances permit if we believe that harm to the environment, people and wildlife will be minimised.
“If the applicant can demonstrate that the varied permit will meet all of the legal requirements, including those for the use of Best Available Techniques, public radiation dose and wildlife radiation dose, then we are legally obliged to grant the application.”