A pneumatic tire (12; 42) for a two-wheeled automotive vehicle, the pneumatic tire (12; 42) comprising: a tread ; a pair of sidewalls ; a pair of beads (18; 44); and a carcass , wherein the sidewalls extend inward from ends, respectively, of the tread in a radial direction, the beads (18; 44) are disposed inward of the sidewalls , respectively, in the radial direction, the carcass is extended on and between one of the beads (18; 44) and the other of the beads (18; 44) along inner sides of the tread and the sidewalls , the carcass includes a first ply and a second ply that is layered radially outward of the first ply , the first ply is turned up around the beads (18; 44) from an inner side toward an outer side in an axial direction, and, by the first ply being turned up, the first ply includes a main portion and turned-up portions , and the second ply is turned back around the beads (18; 44) from the outer side toward the inner side in the axial direction, and, by the second ply being turned back, the second ply includes a main portion and turned-back portions such that turn-back ends of the turned-back portions of the second ply are each disposed inward of the beads (18; 44) in the axial direction, and, the first ply is layered over outer surfaces of the beads (18; 44) and is turned-up; outer ends of the beads are positioned inward of the ends, respectively, of the tread which are axial ends of a tread surface, in the radial direction; characterized in that the main portion and each of the turned-up portions of the first ply are layered between the outer end of the bead and the end of the tread, in the radial direction, such that the turned-up portions have turn-up ends positioned at the radially outer ends of the turned-up portions and disposed inward of the tread , and, at the radially outside of the ends of the tread . a tread ; a pair of sidewalls ; a pair of beads (18; 44); and a carcass , wherein the sidewalls extend inward from ends, respectively, of the tread in a radial direction, the beads (18; 44) are disposed inward of the sidewalls , respectively, in the radial direction, the carcass is extended on and between one of the beads (18; 44) and the other of the beads (18; 44) along inner sides of the tread and the sidewalls , the carcass includes a first ply and a second ply that is layered radially outward of the first ply , the first ply is turned up around the beads (18; 44) from an inner side toward an outer side in an axial direction, and, by the first ply being turned up, the first ply includes a main portion and turned-up portions , and the second ply is turned back around the beads (18; 44) from the outer side toward the inner side in the axial direction, and, by the second ply being turned back, the second ply includes a main portion and turned-back portions such that turn-back ends of the turned-back portions of the second ply are each disposed inward of the beads (18; 44) in the axial direction, and, the first ply is layered over outer surfaces of the beads (18; 44) and is turned-up; outer ends of the beads are positioned inward of the ends, respectively, of the tread which are axial ends of a tread surface, in the radial direction; characterized in that the main portion and each of the turned-up portions of the first ply are layered between the outer end of the bead and the end of the tread, in the radial direction, such that the turned-up portions have turn-up ends positioned at the radially outer ends of the turned-up portions and disposed inward of the tread , and, at the radially outside of the ends of the tread . <EOS>