The problem of resonance absorption is investigated for materials in which the absorber is lumped in small grains imbedded in a matrix of moderator. The point of departure is to take the grains themselves as the fundamental elements in heterogeneous geometry. It is important to treat correctly the mutual shielding between the grains, that is, the Dancoff correction. Introduction of this correction solves immediately the case of macroscopically homogeneous assemblies. The result can be expressed in terms of “shielded” cross sections for the lumped absorber. Utilization of this concept permits also the treatment of additional macroscopic heterogeneities. Existing calculational methods can be employed if the macroscopic heterogeneities are treated with the help of the equivalence relations, and this procedure permits an adequate comparison between the grain structured and homogeneous compounds. Numerical examples are given in Section IV. The average shielding is nearly linear in the grain size. For grains of ThO2 in a graphite matrix, the reduction is about 15% for grains of 0.06 cm diam. On the other hand, the temperature derivative of the resonance integral is increased slightly, particularly at higher temperatures. One can, therefore, either maintain the Doppler coefficient of reactivity with a reduced resonance absorption or increase the Doppler coefficient for the same resonance absorption.