A model is presented for the expected degree of contact between fibres in isotropic near-planar random fibre networks. The statistics of fibre contact in two-dimensional fibre networks are considered and the expressions derived are developed to allow the fractional contact area in structures formed by the superposition of two-dimensional structures to be derived. These expressions allow the fractional contact area to be expressed in terms of the network porosity only. For thin networks, the fractional contact area may be expressed in terms of network porosity and the expected coverage of the network. Theory permitting the determination of the expected area of one contact and hence the expected number of contacts per fibre is presented also. Good agreement is found between the expressions derived for the fractional contact area and data from the literature. (C) 2004 Kluwer Academic Publishers.