A local plasmon resonance on a metal wedge is studied by using the Meixner approach [J. Meixner, IEEE Trans. Antennas Propag.AP-20, 442 (1972)]. It is found that the singular field behavior of a local plasmon resonance as a function of the distance from the edge of the wedge is sensitive to the wavelength and wedge angle, and ranges from a dramatic increase in amplitude close to its theoretical limit to pure oscillatory behavior with only minor amplitude variation. Field singularities for gold, silver, and aluminum wedges are calculated. It is shown that, unlike an ideal-conductor wedge, the real part of the power index of the electric field singularity does not decrease monotonically as a function of the wedge angle, but has a minimum for some angle depending on the wavelength and material parameters. If the dielectric surrounding the wedge has a positive permittivity equal to the absolute value of that of the metal, and hence satisfies the plasmon resonance condition, then the electric field has a peculiar behavior for a wedge whose shape is close to the flat surface.