We report on the development of a three-dimensional (3D) mesoscale lattice model of the diffusion of small gaseous penetrants in heterogeneous polymers. The model has been applied to the problem of predicting diffusional impedances caused by crystalline regions in semi-crystalline polymers, increasing crystalline volume fraction and increasing crystal anisotropy both serve to reduce the diffusion dramatically. Although the trends observed with two- and three-dimensional lattices are similar, absolute values of impedances are much smaller in the case of the 3D lattice. The importance of using a 3D lattice when attempting quantitative prediction is therefore demonstrated. Validation of the 3D model is presented in the form of a comparison between experimental and model predictions of impedance in polyethylene. Crystals of different size, shape and crystalline volume fractions are used in the validation of the model.