Abstract
We analyze the properties of a mechanical resonator embedded into a quantum SQUID and analyze under which conditions it is possible to realize a resonant coupling between the SQUID and the resonator. We find, within the present technology, how it is possible to tune the system into the regime where the plasma frequency of the SQUID matches the resonator frequency and maximizes the corresponding coupling. In these conditions the doubly degenerate quantum level of the system is split by the coupling between the SQUID and the resonator.