This paper is concerned with the study of the leakage spectra of total gamma rays and fast neutrons from two types of heavy concretes made from local magnetite ores. The two types are the steel-magnetite concrete (ρ=5.11 g/cm3) and the basalt-magnetite concrete (ρ=3.05 g/cm3). The radiation source used was a collimated beam emitted from one of the horizontal channels of the ET-RR-1 reactor. Total gamma rays and fast neutrons were measured using a gamma-neutron spectrometer with a stilbene scintillator. Gamma ray or neutron events were rejected by a pulse shape discriminator based on the zero cross over method. The obtained data were displayed in the form of spatial fluxes and energy distributions and attenuation curves. The linear attenuation coefficients for total gamma rays, macroscopic removal cross sections for fast neutrons and half-value layers for gamma rays and neutrons have been obtained for the whole energy range and at different energies. Comparison with other published data has been done when such data are available. For comparison, the steel-magnetite concrete is a much better radiation attenuator than the magnetite and basalt-magnetite concretes, especially for thick shields.