Quality factor of Contour Mode Resonators (CMR) are mainly affected by energy losses due to acoustic waves leaving the resonator through the anchors. An engineering of the anchors in order to create a periodic variation in the acoustic impedance of the material, structures known as Phononic Crystals (PnCs), can help improve the Q factor by reflecting part of the acoustic waves. During this project, FEM models have been validated for both 1D and 2D PnCs. The behavior of the band diagram and quantification of transmission has been studied for three different PnC geometries: circle, cross and square unit cell. Parameters such as unit cell size, filling factor, material composition, thickness and number of repetitions have been varied and comparisons between transmission graph and band diagram allowed to understand better the nature of the modes. It has been found that a linear approximation can predict with a good precision the position of the band gap as a function of the unit cell size. These studies have been done in order to select the best configuration for a future integration on the substrate of a CMR whose frequency range of operation is situated between 200MHz and 500 MHz. The results obtained report a better attenuation and broader peak of attenuation for a cross unit cell made out of AlN and an attenuation increasing linearly with the number of repetitions.