Using a cell model to describe a fibrous porous medium theoretical expressions ale deduced relating effective gas diffusivity to the volume fraction of the fibres. Cylindrical as well as band-shaped fibres are studied. The new models, which are based on solutions to the diffusion equation, agree well with existing correlations. The models are compared with experimental data for water vapour diffusion through sheets of nonwoven fabric and of paper. Diffusion through a nonwoven material consisting of viscose fibres is predicted well by the present model for diffusion around cylindrical fibres. Diffusion through some paper structures such as pulp sheets and handsheets of unbeaten pulp is adequately described by the present model for band-shaped fibres. For newsprint sheets the measured rate of diffusion is much slower than that predicted by either of the models. One explanation for the disagreement between experiment and model for newsprint could be the presence of fine material and fillers in the pores.