The multiferroic behavior of rare‐earth manganites is studied within a microscopic model including a symmetry‐allowed magnetoelectric coupling between polarization and magnetization. The magnetic subsystem is described by a frustrated Heisenberg spin model, whereas the ferroelectric subsystem is characterized by an Ising model in a transverse field. Using Green's function method we find analytically the temperature and wave vector dependent elementary excitation of the magnetoelectric system, the polarization and the magnetization for different magnetoelectric coupling strengths. The system undergoes a magnetic transition at TN and a further reduction of the temperature leads to a ferroelectric transition at TC