The linear-elastic response of single-ply triaxial weave fabric composites is modelled in terms of a homogenized Kirchhofi plate. The ABD matrix for this plate is computed from an assembly of transversely isotropic three-dimensional beams whose unit cell is analysed using standard flnite-element analysis, assuming periodic boundary conditions. A subset of the analytical results is validated by means of careful experiments. It is shown that this simple unit cell beam model captures accurately the experimentally observed behaviour.