A harvesting machine includes a harvesting header with a header frame, a flexible cutterbar assembly attached to the header frame along the length thereof and configured to cut a crop, and a draper assembly positioned behind the cutterbar assembly and operable to receive severed crop material from the cutterbar assembly. The draper assembly includes a fore-and-aft draper and side drapers, with at least part of the draper assembly being rigidly supported on the header frame. A center section of the cutterbar assembly is rigidified so as to be restricted from flexing, while the side sections of the cutterbar assembly flex and follow the changes in terrain.