This paper presents a study of the influence of the geometric shape on the resonance frequency of the artificial magnetic conductor (AMC) by analysis of the electric field distributions on top of the surface metallic patch inside the unit cell. It is known that various parameters such as geometry, dielectric substrate thickness, gap between patches, length and width of patch, size of unit cell, permittivity and permeability strongly affect the resonance frequency. In attempts to elucidate the miniaturization process, as reference, a metallic square patch with a unit cell of size 10 mm × 10 mm was simulated and a resonance frequency of 5.75 GHz was obtained. The device has illuminated by a plane wave with polarization in the y direction. Additionally, different geometries were performed such as triangle, hexagon, circle and cross of Jerusalem. We realized that the field distribution can be used as an physical insight to understand the AMC miniaturization process. In particular, bow-tie geometry provided considerable electrical miniaturization compared with square patch, about 1.5 GHz. The results are supported by finite element method. Our findings suggest that shift at resonant frequency may be interpreted as a variation in the net induced electric polarizability on the surface of the metallic patches.