A system for presenting an aerial display over an audience of spectators. The system includes a plurality of unmanned aerial vehicles (UAVs) and a plurality of flexible projection screens. Each of the screens is supportable in a display air space by the UAVs. The system includes a ground control system with a processor executing a fleet manager module and with memory storing a different flight plan for each of the UAVs. During operation during a display time period, the UAVs execute the flight plans to move and to position the flexible projection screens within the display air space. The flexible projection screens each may include a mesh body configured to have low wind resistance and to provide a projection surface for reflecting light. The system may include a projector projecting light onto the projection surface of at least one of the flexible projection screens during the display time period.