<p>Membranes are widely used in the devices construction for biomedical prostheses, architectural and civil structures (bridge, roof, radio antennas, optical reflectors etc.), and therefore, their studies are crucial to maintain integrity and reliability of such devices. Various reports characterize resonance as a critical phenomenon that is directly related to the reliability of the membrane. However, closed form mathematical solutions discussing resonance position, corresponding force, impact of frequency, etc. are sparse in literature. In that context, here, we develop closed form analytical solution for resonance conditions in a fixed edges rectangular vibrating membrane using series solution of its differential equation model. Additionally, we visualize the analytic solution numerically under different frequencies and external force conditions. We find that the results from developed closed form solutions agree well with the numerical experiments, however, within reasonable error limits. Notably, we observe that vibration can have finite to unbounded amplitude (destruction of the membrane), slow swing to shake if position of the external force is varied. Due to the unavailability of results from physical examination under similar constraints, we also propose an extension of the available experiments that could be used for validation and strengthen the model discussed in the paper.</p>