A model equation for the oscillation of a pressurized gas bubble in a nonlinear incompressible elastic medium [Emelianov et al., J. Acoust. Soc. Am. 115, 581 (2004)] is extended to include effects of surface tension, viscosity, weak compressibility, and confinement by an elastic shell. The significance of this work is that starting from first principles, the full nonlinearity of the incompressible elastic medium surrounding the bubble and forming its shell is taken into account. Measurements of equilibrium radius as a function of external pressure for a gas bubble in a tissue-like gel are also presented. A general approach to including hysteresis is also discussed.