The numerical analysis of large numbers of arbitrarily distributed discrete thin fibres embedded in a continuum is a computationally demanding process. In this contribution, we propose an approach based on the partition of unity property of finite element shape functions that can handle discrete thin fibres in a continuum matrix without meshing them. This is made possible by a special enrichment function that represents the action of each individual fibre on the matrix. Our approach allows to model fibre-reinforced materials considering matrix, fibres and interfaces between matrix and fibres individually, each with its own elastic constitutive law. Copyright © 2010 John Wiley & Sons, Ltd.