Design of novel, portable and aurally undetectable cryogenically cooled infrared imagers often relies on compliant vibration protective pads for mounting the integrated dewar-detector-cooler assembly upon the imager's enclosure. Extensive analytical study and experimental effort have shown that for the best acoustic performance the visco-elastic properties of such pads need to be matched with the dynamic properties of the typically undamped enclosure, subjected to the tight limitations imposed on the low frequency cooler-induced line of sight jitter resulting from the oscillations of the gasodynamic torque and compliance of the above pads. Unfortunately, the regular approach to a design of the optimal vibration protective pad does not seem to exist. As a result, the development of the suitable vibration protective pad is widely regarded as a purely empirical process and requires a great deal of experimental trial-and-error effort. The authors are attempting to apply the regular finite element modeling approaches to an optimal design of such vibration protective pads. In doing so, they are making use of the full finite elements models of infrared imager enclosure with vibration mounted integrated dewar-detector-cooler assembly. The optimal geometry and dynamic properties of a compliant layer of vibration protective pad are evaluated using the optimisation procedure with purpose of attenuation the volume velocity of the active radiating surface. The theoretical findings are in fair agreement with the outcomes of the full-scale experimentation.