Abstract A magnon and a phonon are the quanta of spin wave and lattice wave, respectively, and they can hybridize into a magnon polaron when their frequencies and wavenumbers match close enough the values at the exceptional point. Guided by an analytically calculated magnon polaron dispersion, dynamical phase-field simulations are performed to investigate the effects of magnon polaron formation on the attenuation of a bulk acoustic wave in a magnetic insulator film. It is shown that a stronger magnon–phonon coupling leads to a larger attenuation. The simulations also demonstrate the existence of a minimum magnon–phonon interaction time required for the magnon polaron formation, which is found to decrease with the magnetoelastic coupling coefficient but increase with the magnetic damping coefficient. These results deepen the understanding of the mechanisms of acoustic attenuation in magnetic crystals and provide insights into the design of new-concept spin interconnects that operate based on acoustically driven magnon propagation.