The dip coating of a fiber of small radius is studied via a finite element solution of the Navier-Stokes equations. The coating speed is selected within the range corresponding to the visco-capillary and visco-inertial regimes. Predictions obtained within the range of the visco-capillary regime are in very good agreement with the Landau-Levich law and with published experiments, whereas those obtained within the visco-inertial regime-that is, at coating speeds typical of industrial applications match published experimental data.