Heavy concrete is a promising candidate material for a fusion reactor shield. It provides strong shielding performance, though it has a heterogeneous structure due to random arrangement of the heavy aggregates contained as absorbers. To obtain data for future fusion reactor shield designs, D-T neutron irradiation experiments using both heterogeneous and homogeneous heavy concrete samples were carried out to investigate how much the heterogeneity due to the aggregates affects shield performance. Leakage neutron spectra and reaction rates of activation foils were measured, and they were compared with the analyses by the Monte Carlo code MCNP-CFP. From the comparison of results, the measured heterogeneity effect was well reproduced by MCNP-CFP, though there was a slight disagreement in the thermal region. For a point neutron source, a heterogeneous shield was found to be advantageous compared with a homogeneous one from the standpoint of shielding performance above 1 MeV. This conclusion was exactly opposite to what was anticipated. Analysis of the results confirmed that the effect was strongly associated with the manufacturing process used for the heavy concrete. For thermal neutrons, a homogeneous shield is still regarded to be most preferable. To suppress the heterogeneity effect above 1 MeV, it is necessary to use a sufficiently large heavy concrete shield. Then analysis with a conventional calculation method is feasible except for the thermal neutron region. If a smaller shield is employed, a specialized Monte Carlo code with a heterogeneous treatment like MCNP-CFP should be used for the precise analysis.