The dynamics of electromagnetoactive polymer (EMAP) membranes have attracted much attention recently because of their wide range of modern robotic applications. Such applications majorly centered on how the dynamics of this novel class of membranes are affected by the mechanical behavior of the compliant electrode. This article presents the dynamic modeling and analysis of EMAP membranes, examining how the inertia of the electrode, coupled with its inherent viscoelastic properties, impacts its dynamic performance. Both the compression and suspension stages of the membrane are covered here in broad terms. An Euler–Lagrange equation of motion is implemented to deduce the governing dynamic model equation of the membrane system. The findings of the model solutions provide preliminary insights to characterize the dynamic response, instability analysis, periodic behavior, and resonance properties across varying parameters such as inertia, electric field, magnetic field, and prestress. Moreover, the study also evaluates the periodicity and stability of the nonlinear oscillations using Poincaré maps and phase portraits, facilitating an assessment of quasi-periodic to periodic transitions.