Numerical simulations of the interaction of optical fields with metal tips, such as in photofield emission and laser-assisted scanning tunneling microscopy, show that the electric field at the apex of the tip is much greater than that in the incident optical beam. Calculations were made using the method of moments with two models of the tip; a conical frustrum with hemispherical end caps, and a paraboloid. A large number of subvolumes (850-1000) was used to decrease the errors caused by finite matrix size with the method of moments, and it is shown that these errors have no significant effect on the results. The ratio of the optical electric field at the apex of the tip to that in the incident beam (field ratio) varies directly with the curvature at the apex, and is increased by raising the tip length and the optical wavelength. For the range of parameters used in the examples field ratios of 3-15 dB were found for incidence normal to the tip axis, and values as large as 32 dB were found for an angle of approximately 10 degrees between the incident laser beam and the tip axis. Differences between the results for the two models and the dependence on the radius bf curvature show that the field ratio must vary greatly from tip to tip.