Previous studies on electric and elastic behaviors induced by internal or surface electrodes in a piezoelectric ceramic are mainly concentrated on a two-dimensional analysis. However, most sensors and actuators are related to a three-dimensional piezoelectric body with electrodes. This paper is concerned with the electroelastic analysis of a penny-shaped thin electrode coating on the surface of a hexagonal piezoelectric half-space. The Hankel transform technique is employed to reduce the mixed boundary value problem to an Abel integral equation. Solving the resulting equation analytically, a solution is obtained in a closed form. Explicit expressions for the complete electric and elastic behaviors in any position in the entire piezoelectric half-space are determined in terms of elementary functions. The results indicate that the vertical surface displacement reaches a maximum at the entire electrode region, while the radial surface displacement reaches a peak only at the electrode edge. Moreover, in addition to electric displacement and electric field, elastic stresses exhibit singular behavior near the electrode edge.