EBG antennas are very thin and high gain antennas. They provide a great control of the power radiated. The antennas studied in this paper are realised with periodic dielectric materials. Classically they present directive patterns for one frequency band, but it is possible to design them to radiate directive patterns for multiple frequency bands. The methodology is described. It is also possible to control the direction of the radiated beam with this kind of periodic structure. This article explains how, with an appropriate feeding it is possible to control the direction of propagation and to create one main lobe. This technique is explained.