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To overcome the physical limitations of electrically small antennas, strain-mediated magnetoelectric antennas have been studied experimentally and theoretically. However, current closed-form analytical models include solely one-dimensional approaches. This paper proposes a two-dimensional closed-form analytical model of a laterally-excited multiferroic antenna. To model thickness-shear vibrations, we propose an extended Mason model to two dimensions. This theory solves unidirectionally-coupled elastodynamics-magnetization dynamics-electrodynamics. Without using the infinitesimal dipole approximation, this model provides a closed-form solution of the radiated electromagnetic field with an explicit dependency of the antenna response on the physical parameters, enabling their optimization. Furthermore, we compare the efficiency-bandwidth product of different multiferroic antennas with Chu's limit in the Akhiezer regime, which delimits the highest achievable mechanical quality factor for acoustic resonators at GHz frequencies. We show that phonon-phonon coupling of Akhiezer damping is most likely to limit multiferroic antenna radiation, not Chu's limit. Moreover, judicious choice of materials can enhance the maximum efficiency by more than an order of magnitude.