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Pressure thresholds for inertial cavitation in water and biological media modeled as a viscous fluid are calculated using a numerical implementation of the Gilmore equation for adiabatic bubble oscillations. The threshold criterion is chosen to be a bubble collapse temperature of 5000 K in order to facilitate comparison with the analytical theory of others. There is a trend toward increasing pressure thresholds with increasing frequency and/or viscosity. The frequency dependence of the inertial cavitation pressure threshold becomes more pronounced as the fluid viscosity is increased. There is a clear indication of two regimes of bubble behavior in which "small" and "large" bubbles exhibit elevated thresholds due to surface tension and mass loading, respectively. The "nonlinear resonance size" demarcates these two regimes and provides a descriptor of the initial bubble sizes most likely to undergo inertial cavitation for a given frequency and viscosity. The physical effects of the liquid's viscosity on the subsequent bubble dynamics are discussed and comparison made with experimental measurements.