An experiment is presented in which a model fibre-reinforced composite undergoes squeeze-flow. Results are presented for two different fibre lay-ups over a range of fibre volume fractions. The response of the material is an initial rapid compression followed by a limiting deformation and a key feature of the experimental tests is their reproducibility. The experimental results show poor agreement with existing analytical treatments of the problem in which the material is modelled as an anisotropic continuum. Consequently, a two-dimensional finite element approach is developed in which the composite is treated as a Newtonian fluid containing cylindrical voids that represent the fibres and convect with the fluid.