In this thesis results obtained by a simplified discrete model of a single cell of an active metamaterial are analysed and discussed. The active metamaterial cell of geometry suitable for 3D printing with a simple device is assumed: a tube of rectangular cross-section periodically intermitted by a number of double membranes. Equations of motion and the corresponding transfer functions for the discrete linear dynamic model for a tube with two double membranes and two actuators are derived, assuming that the dynamics of each of the membranes and rectangular acoustic cavities between them can be approximated by their first vibration mode only, i.e. by a mass-spring system for the membrane and a spring-damper system for the acoustic cavity. The obtained four DOF (degree of freedom) model is analysed and discussed with respect to the stability of the feedback loop using the Routh-Hurwitz stability criterion. Parameters of the passive system which guarantee the stability of the active system when the two feedback loops are closed have been determined. Furthermore, for stable systems, a loss of acoustic reciprocity in a wide range of frequencies is shown. The reciprocity loss is quantified by comparing the corresponding pairs of a total of 16 derived transfer functions between forces and vibration velocities of each of the four masses in the discrete mechanical system. Therefore, it is expected that the future results obtained by simulations on an active vibroacoustic system with distributed parameters, as well as experimentally obtained results, would confirm a significant loss of acoustic reciprocity.