Plasmonic field enhancement in a fully coated dielectric near field scanning optical microscope (NSOM) probe under radial polarization illumination is analyzed using an axially symmetric three-dimensional (3D) finite element method (FEM) model. The enhancement factor strongly depends on the illumination spot size, taper angle of the probe, and the metal film thickness. The tolerance of the alignment angle is investigated. Probe designs with different metal coatings and their enhancement performance are studied as well. The nanometric spot size at the tip apex and high field enhancement of the apertureless NSOM probe have important potential application in semiconductor metrology.