Pneumatic tire 1 for an agricultural machine, having an axis of revolution XX and comprising a tread 7, a sole 11 situated opposite the tread 7, and two sidewalls 13, 15 connecting the tread 7 to the sole 11. The tread 7, the sole 11 and the two sidewalls 13, 15 together form a casing 17 defining a chamber 19 inside the pneumatic tire 1. At least one of the sidewalls 13, 15 comprises, in this order and in succession in a direction oriented radially from the axis of revolution XX to the outside, a proximal portion 131, an intermediate portion 133 and a distal portion 135. In the unloaded state, the intermediate portion 133 projects into the chamber 19 in a direction substantially parallel to the axis of revolution XX.