A hoop tread, radial carcass flotation tire is constructed in accordance with a method and through the use of apparatus which impart controlled carcass flexing characteristics while accommodating axle drive of the tire. The method includes constructing a tire carcass with radially directed cords in sidewall portions and with circumferentially directed cords in a tread face portion. The apparatus comprises a mandrel assembled by mounting a plurality of segments about an axle and used to support plies of material during carcass construction. The tire is capable of "floating" over loose or easily damaged supporting surfaces including growing crops in agricultural fields without injury or damage to the supporting surface.