In this study large-eddy simulations (LES) are used to gain more knowledge on the shell of subsiding air that is frequently observed around cumulus clouds. First, a detailed comparison between observational and numerical results is presented to better validate LES as a tool for studies of microscale phenomena. It is found that horizontal cloud profiles of vertical velocity, humidity, and temperature are in good agreement with observations. They show features similar to the observations, including the presence of the shell of descending air around the cloud. Second, the availability of the complete 3D dataset in LES has been exploited to examine the role of lateral mixing in the exchange of cloud and environmental air. The origin of the subsiding shell is examined by analyzing the individual terms of the vertical momentum equation. Buoyancy is found to be the driving force for this shell, and it is counteracted by the pressure-gradient force. This shows that evaporative cooling at the cloud edge, induced by lateral mixing of cloudy and environmental air, is the responsible mechanism behind the descending shell. For all clouds, and especially the smaller ones, the negative mass flux generated by the subsiding shell is significant. This suggests an important role for lateral mixing throughout the entire cloud layer. The role of the shell in these processes is further explored and described in a conceptual three-layer model of the cloud.