We have performed numerical analysis of localized surface plasmons (LSP) at a nano silver particle on a glass substrate using the finite-difference time-domain method, taking into account the size dependence of the dielectric constants of silver. It was found that the characteristics of LSP at a nano metal particle depend on both shapes of the particles and a dielectric constant of the substrate. In calculations, we employed the geometry in which a nano-particle was located on a glass substrate, the area of calculations. The three types of particles were assumed: a sphere, a spheroid and a hemisphere. In spheroid, the aspect ratio of particles R, is changed from 1.0 to 2.0. For the normal incidence to the spheroid, i.e., the long-axis, the characteristics of LSP are insensitive to R compared. It was observed the red-shift of LSP resonance wavelength and the field enhancement due to the mirror image in the substrate. For spheres and spheroid, the strong enhancement of the z-component field was observed on the substrate. For the hemisphere, we have found the strong localization of the field along the edge of the hemisphere and the strong enhancement of the x-component field was observed on the surface of the substrate.