The calculation of effective cross sections for materials with grain structure has been investigated. A method is outlined based on Sauer's formalism that is not restricted to loosely packed grains and small ratios of scattering to total cross sections, in contrast to the treatment based on isolated grains reported earlier by Dyos and Pomraning. The method is applicable for GAROL type resonance calculations, i.e., resonance treatments based on an explicit calculation of the detailed energy spectrum, as well as for reactor cell calculations at thermal energies. As an example, the grain shielding factors for 400 µ ThC2 grains in a carbon moderator have been calculated as energy-dependent quantities through the 21.8 and 23.5 eV thorium resonances at 300°K. The results are compared with a GAROL reference calculation (set up for the grains) and with the method given by Dyos and Pomraning. The maximum error for the energy-dependent grain shielding factors in the present method is 1.3% compared with 11.3% in the method of Dyos and Pomraning. Application of the present method at thermal energies on 200-µ PuO2 grains embedded in a carbon moderator yields energy-dependent grain shielding factors that differ by <1% from a S8-P1 multigroup reference calculation.