Application of artificial ground planes in design of compact cavity-resonance dual-band high-gain antennas is presented. The artificial ground plane consists of periodic strip grating on grounded dielectric slab. A code based on method of moment (MoM) is developed to analyze and design such artificial ground planes. The reflection parameters obtained using the MoM code are employed to characterize the surface impedance of the artificial ground plane for different incident angles and both TE and TM polarizations. Then, this impedance surface is used in transverse equivalent network (TEN) model of the cavity-resonance antenna with high-permittivity dielectric superstrate. Using TEN model radiation properties of such antennas are analyzed. Finally, the antenna with the compact size is designed to demonstrate the maximum directivity. An interesting characteristic of this antennas is that when the antenna ground plane acts as an artificial magnetic conductor the height of the antenna is almost reduced by a factor of two, while its directivity is increased by about 1 dB compared to the conventional antennas of this class having PEC ground plane.