The method developed for the calculation of the flux and composition of the West Area Neutrino Beam used by NOMAD in its search for neutrino oscillations is described. The calculation is based on particle production rates computed using a recent version of FLUKA and modified to take into account the cross-sections measured by the SPY and NA20 experiments. These particles are propagated through the beam line taking into account the material and magnetic fields they traverse. The neutrinos produced through their decays are tracked to the NOMAD detector. The fluxes of the four neutrino flavours at NOMAD,are predicted with an uncertainty of about 8% for v(mu) and v(e), 10% for (v) over bar (mu), and 12% for (v) over bar (e). The energy-dependent uncertainty achieved on the v(e)/v(mu) prediction needed for a v(mu) --> v(e) oscillation search ranges from 4% to 7%, whereas the overall normalization uncertainty on this ratio is 4.2%.