A compact dual band antenna made of high dielectric constant substrate is studied. Embedding a higher dielectric cylindrical inside the substrate host cylindrical enhances the dual band behaviour. The first part displays the characteristics of single CRDA as return loss, bandwidth and radiation pattern, then, the second part describes the aim of using an antenna, composed by the arrangement of two cylindrical resonators in which the smallest is inserted in the largest, to lead dual-frequency behaviour, and achieve a dual-band antenna. The proposed antennas are investigated using Finite Element Method (FEM), the impedance matching dual band definition and covers the Ultra High Frequency band (UHF).