A voxel-based meshing technique is introduced for three-dimensional woven fibre composites. It offers a simple and computationally efficient method of meshing fibre tows and matrix, including material boundaries, for specimens of any size and thickness. Voxel element mesh geometry is validated against input in the form of a tetrahedral mesh generated exploiting a Delaunay formulation that utilises statistically representative tow information. Voxel meshes show excellent agreement with the more complex tetrahedral mesh for the prediction of surface displacements upon uni-axial loading, including the presence of displacement discontinuities at tow boundaries that may indicate damage initiation sites. A study is conducted to investigate the variation in matrix thickness and the subsequent effect on surface geometry and displacements. This found an increase in matrix thickness substantially reduces the presence of displacement discontinuities, thus reducing the likelihood of strain-induced cracking in these regions.