  We study the dynamics of Josephson Parametric Amplifier (JPA) coupled to a
mechanical oscillator, as realised with a dc Superconducting Quantum
Interference Device (SQUID) with an embedded movable arm. We analyse this
system in the regime when the frequency of the mechanical oscillator is
comparable in magnitude with the plasma oscillation of the SQUID. When the
nano-mechanical resonator is driven, it strongly affects the dynamics of the
JPA. We show that this coupling can considerably modify the dynamics of JPA and
induce its multistability rather than common bistability. This analysis is
relevant if one considers a JPA for detection of mechanical motion.
