A radial ply tire having structure thereon for minimizing the wear characteristic of the lateral edges of the tread. The tire has a central zone which consists of a curved surface at a radius R.sub.1 to a specified distance from the centerline of the tire and a curved surface at a radius R.sub.2 over the near-shoulder zones from the lateral edges of the central zone to a lateral boundary of the lateral shoulder on the tire. The near-shoulder zones on the tire have an intermediate position C thereon located at a specified distance (W.sub.1) from the center line so that the specified position (W.sub.1) is also spaced a further specified distance (d) radially outward from a position (A) located at the aforesaid specified distance (W.sub.1) on an imaginary curved surface extrapolated from the radius of curvature R.sub.1.