Enhancement of devices operating frequency and size reduction are actual challenges in the field of electroacoustic devices development. Piezoelectric resonators showing small size and high Q at GHz range frequency can be fabricated by exploiting the diamond and piezoelectric AlN film technology. The main objective of this paper consists of the modelling study of the Lamb modes propagation in diamond/AlN thin suspended membranes. The membrane consists of a piezoelectric AlN layer, 3.6 μm thick, on top of a diamond  suspended membrane  10 μm thick. This device can be obtained by  standard technological processes, such as the backside Si/diamond/AlN micro-machining: the diamond layer plays the role of a back-etching stop layer, allowing the release of a diamond/AlN suspended membrane.   Disperse software was used to calculate the phase and group velocity dispersion curves of the Lamb modes in diamond/AlN structures. The zero group velocity (ZGV) resonant conditions in the diamond/AlN composite plate, i.e. the frequencies where the mode group velocity vanishes while the phase velocity remains finite, were found. By means of FEM analysis, the propagation of acoustic Lamb waves in the layered structure AlN/diamond has been investigated:  the elastic displacement fields within the composite plate  at frequencies up to 9000 MHz, as well as the wave lengths were calculated, and the acoustic wave types (quasi-symmetric and quasi-antisymmetric modes) of the ZGV points were identified. The ZGV points of a Lamb mode device are associated with an intrinsic energy localization under the metal electrodes: this fact enables the design of acoustic micro-resonators employing only one interdigital transducer (IDT) and no reflectors, thus reducing both the device size and the technological complexity, while the energy confinement is a natural consequence of the selected acoustic mode. At the ZGV points, the mode energy is locally trapped in the source area thus these modes are expected to be highly sensitive to the plate thickness and mechanical properties changes; the applicability of the ZGV resonators for gas sensing was studied.