The microstructure of fine coal filter cakes governs their formation rate and dewaterability, which are both critical to the efficient beneficiation of fine coal. However, the principles by which the microstructure influences the transport properties of filter cakes are not well understood, partly due to the difficulty in obtaining information about the three-dimensional morphology of their pore structure. The paper describes an example of application of the Boolean model that leads to a straightforward and realistic quantification of the three-dimensional microstructure of fine coal filter cakes. Such a model is extremely attractive, for (1) it relies on well-established random set theory, (2) its characterisation involves standard image analysis of polished sections, and (3) no empiricism is involved. Although the model was found to be ideally suited to the characterisation of fine coal filter cakes, the flexibility of its underlying theory makes it an excellent candidate for quantifying other porous media. Such a model not only permits easy access to the three-dimensional details of porous media, but also holds promise for assisting in predicting the transport properties of porous media because of its realism. Subsequent publications will discuss applications of the model to obtain three-dimensional computer simulations of filter cakes, and to predict single-phase permeability of filter cakes.