This paper presents the results of comprehensive laboratory work conducted for investigating the mechanical and radiation attenuation characteristics of heavyweight concrete produced with pyrite, chromium, and magnetite aggregates and normal weight concretes produced with three different water/ cement (w/c) ratios. Various experiments were conducted to determine the compressive strengths, ultrasound transmission velocities, experimental elasticity modules, and mass attenuation coefficients of these concretes. Heavy and normal weight concretes exhibited similar behaviour in terms of compressive strength and elasticity modules. In heavyweight concretes, with increased w/c ratios (by keeping the amount of water constant and decreasing the amount of cement), the corresponding density increased due to the increase in the amount of high-density aggregates rather than cement in the composition of concrete. Thus, heavyweight concretes produced with a high w/c ratio and low strength can absorb more X-rays. Mass attenuation coefficients converge in heavy and normal weight concretes with different densities at high energy levels.