X-ray micro-computed tomography (microCT) is a non-destructive method of visualising specimens in three dimensions at the micrometer scale. Finite element analysis (FEA) is a method for approximating the structural response of systems to mechanical loading. The two methods are readily combined in micro-finite element analysis (microFEA). The microCT image, already in the discretized form of voxels, can be directly converted into a finite element mesh allowing materials with complex microstructures to be modelled. In this paper we present an example of microFEA model construction and use in the study of coke, a porous mineral. MicroCT datasets of different coke blends were used to create finite element models. The models were used to examine the material's structural response to compressive loading by studying the resultant stress distributions and material deformation. MicroFEA can be used to advance our understanding of the relationship between porous materials' microstructure and their bulk properties.