Monte Carlo simulations are conducted in two and three dimensions to compute the diffusion coefficients of gas molecules permeating membranes containing oriented platelets. The effects of platelet aspect ratio, relative separation, loading and spatial dimension are examined. The model of Aris [R. Aris, On a problem in hindered diffusion, Arch. Ration. Mech Anal. 95 (2) (1986) 83-91] is shown to correlate well with a 2D Monte Carlo simulation. However, the Aris model, when compared to a 3D simulation, over-predicts the barrier-effect of filler, by 50% in some cases. Additionally, flaws in idealized geometries for 3D models are addressed and a new 3D geometry is presented. The results have particular value for nanocomposite films at low platelet loadings. (c) 2005 Elsevier B.V. All rights reserved.