\begin{abstract}
Recent full hydrodynamic simulations of a sonoluminescing bubble interior
have shown that the bubble content is compressed to a very dense state 
during the violent collapse.  In this paper, we numerically studied the 
shape stability of a radially oscillating gas bubble by using 
Hilgenfeldt {\it et al.} theoretical model with corrections taking into
account the gas density effect. Our results show that gas density
variations not only significantly suppress the Rayleigh-Taylor
instability, but also enhance the threshold of the parametric instability
under sonoluminescence conditions.
\end{abstract}