Nuclear power plants and research purposed reactors produce spent nuclear fuel, which leads to a need for safe spent fuel management and radiation protection. Traditionally, concrete with the addition of different aggregates has been the primary material for shielding against radiation and is used also for transport and storage of radioactive waste. Despite these applications, there is still a need to develop new composite materials that will preserve the radiation shielding properties of concrete, while offering superior mechanical and also cost effective benefits. This article investigates the radiation shielding properties of HI-STORM containers, made of a new composite material, and reinforced with basalt-boron fibre for human and environment protection. In the concrete recipe, part of the cement is replaced by oil shale ash with cementitious characteristics. The formulation of concrete reinforced with basalt-boron fibre (with the addition of 6% boron oxide) is presented. Oil shale ash (OSA) is a class-C fly ash, a by-product in the energy production process. OSA can be used as a partial replacement to cement in concretes, thanks to its cement-like qualities and low carbon content, which contributes to a reduction in the overall CO2 footprint of concrete. In our investigated concrete mixes 5 to 35% of cement was replaced by OSA (Electrostatic Precipitator Ash) coming from Auvere (Estonia) thermal power plant. Using the Monte Carlo method, the Serpent code was used to simulate the passage of neutron radiation through a composite material to assess its biological shielding properties. It is shown that the addition of basalt-boron fibre to concrete improves the protective properties of biological shielding against neutron radiation.