Although convective clouds are known to generate internal gravity waves, the mechanisms responsible are not well understood. The present study seeks to clarify the dynamics of wave generation using a high-resolution numerical model of deep convection over the Tiwi Islands, Australia. The numerical calculations presented explicitly resolve both the mesoscale convective cloud cluster and the gravity waves generated. As the convective clouds evolve, they excite gravity waves, which are prominent features of the model solutions in both the troposphere and stratosphere. The source location is variable in time and space but is related to the development of individual convective cells. The largest amplitude gravity waves are generated when the cloud tops reach the upper troposphere. A new analysis technique is introduced in which the nonlinear terms in the governing equations are taken as the forcing for linear gravity waves. The analysis shows that in the present calculation, neither the shear nor the diabatic heating are the dominant forcing terms. Instead, the wave source is most easily understood when viewed in a frame of reference moving with the wind at the level of neutral buoyancy, whereupon the source may be described as a vertically oriented, oscillating convective updraft. This description is consistent with the properties of the modeled stratospheric waves.