This study focuses on the investigation of elastic wave modes sensitivity in piezomagnetic composite membrane under an applied magnetic field. The piezomagnetic model has been implemented in Comsol-Multiphysics, and has been solved as an eigen-frequency problem. The evolution of the electromechanical resonance frequency of different modes has been investigated as a function of an arbitrary applied DC magnetic field. Both magnitude and direction are considered. We carried out that the sensitivity depends on the mode polarization and on magnetic state of the mageto-elastic film, which in turn depends on the magnetic field's magnitude and orientation. The magnetic field dependence of the resonance frequency is well correlated to the magnetic field dependence of magneto-elastic stiffness constants.