The tire (1) has an axis of revolution. A tread (7) is provided, such that a sole (11) is situated opposite the tread. Two sidewalls (13,15) connect the tread to the sole. The tread, sole and two sidewalls together form a casing that defines a chamber (19) inside the tire. The sidewall has a proximal portion, an intermediate portion and a distal portion in a direction oriented radially from the axis of revolution to the outside. The intermediate portion projects into the chamber in a direction substantially parallel to the axis of revolution in the unloaded state. An independent claim is included for a rolling element for an agricultural machine.
