We investigate numerically the effect of non-condensable gas inside a vapor bubble on the bubble dynamics and the collapse pressure. Free gas in the vapor bubble has a cushioning effect that can weaken the pressure wave and enhance the bubble rebound. In order to access this effect numerically, simulations of collapsing vapor bubbles containing non-condensable gas are performed. In the simulations, the effects of the gas on the rebound and the shockwave energy are monitored for different operating points with varying initial gas contents p_g,0 inside the bubble and driving pressures Δp. For the cavitating liquid and the non-condensable gas we employ a homogeneous mixture model with a coupled equation of state for all components and the cavitation model is a barotropic thermodynamic equilibrium model, which is embedded in a higher order implicit large eddy approach for narrow stencils. Compressibility of all phases is considered, to capture the shockwave of the bubble collapse. The effect of the free gas on the rebound and the dampening of the emitted shockwave by the gas contained in the bubble are well captured by our simulations.