Two families of heavy concrete were investigated in this project, the first containing hematite and the second magnetite aggregates. Boron carbide also replaced cement in mass of 2.5, 5 and 10%. Once again, in these compounds the content of cement was reduced by 5% and replaced by nanosilica. Such parameters as compressive strength, ultrasonic pulse velocity and density were investigated, and the specimens were irradiated with cobalt 60, to quantify the linear attenuation coefficient. Using iron ore aggregate, especially magnetite, was advantageous for all the above-mentioned parameters, while the opposite was true, when boron carbide was added to the mix. The addition of nanosilica compensated the decrease in compressive strength of concrete due to the presence of boron carbide, but reduced the linear attenuation coefficient by about 4%. However, the properties of the mixes containing boron carbide and nanosilica, were always better than those of conventional concretes. To quantify the linear attenuation coefficient, Monte Carlo simulations were performed, and their results turned out to be in good agreement with those obtained by the experimental measurements.