Tyre for a heavy vehicle of the self-propelled agricultural type, comprising: - a tread, of width A, connected by way of two sidewalls to two beads intended to provide a mechanical connection to a rim, of width L, - a reinforcement comprising a crown reinforcement, radially on the inside of the tread, and a carcass reinforcement, radially on the inside of the crown reinforcement, - the carcass reinforcement comprising at least two turned-up carcass layers (71, 72) and at least two non-turned-up carcass layers (73, 74), - each turned-up carcass layer (71, 72) consisting of mutually parallel reinforcing elements and comprising a main part (711, 721) wrapped, in each bead, from the inside of the tyre towards the outside around a bead wire of diameter D, so as to form a turn-up (712, 722) of which the end (E 1, E 2) is positioned radially on the outside of the radially outermost point of the bead wire at a radial distance (a 1, a 2), - each non-turned-up carcass layer (73, 74) consisting of mutually parallel reinforcing elements, the end (E 3, E 4) of which is positioned at a radial distance (b 3, b 4) from the radially outermost point of the bead wire, - the meridian section of the tyre having, in a meridian plane passing through the rotation axis of the tyre, a section height H and a section width S, where the radial distance (a 1, a 2) between the end (E 1, E 2) of the turn-up (712, 722) of each turned-up carcass layer (71, 72) and the radially outermost point of the bead wire is at least equal to 0.5 times the section height H of the tyre, where the radial distance (b 3, b 4) between the end (E 3, E 4) of each non-turned-up carcass layer (73, 74) and the radially outermost point of the bead wire is at most equal to the diameter D of the bead wire, where the at least two non-turned-up carcass layers (73, 74) of the carcass reinforcement are axially on the outside, at the sidewalls, of the main parts (711, 721) of the two turned-up carcass layers (71, 72), and where the end (E 3) of the axially outermost non-turned-up carcass layer is interposed between the respective turn-ups (712, 722) of two turned-up carcass layers (71, 72). - a tread, of width A, connected by way of two sidewalls to two beads intended to provide a mechanical connection to a rim, of width L, - a reinforcement comprising a crown reinforcement, radially on the inside of the tread, and a carcass reinforcement, radially on the inside of the crown reinforcement, - the carcass reinforcement comprising at least two turned-up carcass layers (71, 72) and at least two non-turned-up carcass layers (73, 74), - each turned-up carcass layer (71, 72) consisting of mutually parallel reinforcing elements and comprising a main part (711, 721) wrapped, in each bead, from the inside of the tyre towards the outside around a bead wire of diameter D, so as to form a turn-up (712, 722) of which the end (E 1, E 2) is positioned radially on the outside of the radially outermost point of the bead wire at a radial distance (a 1, a 2), - each non-turned-up carcass layer (73, 74) consisting of mutually parallel reinforcing elements, the end (E 3, E 4) of which is positioned at a radial distance (b 3, b 4) from the radially outermost point of the bead wire, - the meridian section of the tyre having, in a meridian plane passing through the rotation axis of the tyre, a section height H and a section width S,