Despite the importance of fungi in soil ecosystem services, a theoretical framework that links soil management strategies with fungal ecology is still lacking. One of the key challenges is to understand how the complex geometrical shape of pores in soil affects fungal spread and species interaction. Progress in this area has long been hampered by a lack of experimental techniques for quantification. In this paper we use X-ray computed tomography to quantify and characterize the pore geometry at microscopic scales (30 μm) that are relevant for fungal spread in soil. We analysed the pore geometry for replicated samples with bulk-densities ranging from 1.2–1.6 g/cm³. The bulk-density of soils significantly affected the total volume, mean pore diameter and connectivity of the pore volume. A previously described fungal growth model comprising a minimal set of physiological processes required to produce a range of phenotypic responses was used to analyse the effect of these geometric descriptors on fungal invasion, and we showed that the degree and rate of fungal invasion was affected mainly by pore volume and pore connectivity. The presented experimental and theoretical framework is a significant first step towards understanding how environmental change and soil management impact on fungal diversity in soils.