A heavy duty pneumatic tire, comprising: a tread having an outer surface that forms a tread surface; a pair of sidewalls that extends almost inward, in a radial direction, from ends, respectively, of the tread; a pair of beads positioned almost inward of the sidewalls, respectively, in the radial direction; a clinch portion that extends from the sidewalls to the beads, and a carcass ply that is extended, along the tread and the sidewalls, on and between both the beads, wherein each bead includes a core and a bead apex positioned outward of the core in the radial direction, the carcass ply includes a main body portion and turned-up portions which are formed by the carcass ply being turned up from an inner side toward an outer side around the core, and a concave curved surface extends on an outer surface of the clinch portion in a circumferential direction, and the concave curved surface is engageable with a convex curved surface formed on an outer side end, in the radial direction, of a rim flange, a ratio R1/R of a radius of curvature R1 of the concave curved surface to a radius of curvature R of the convex curved surface of the rim flange, satisfies 1.7 ≤ R 1 / R ≤ 2.5, and the radius of curvature R1 of the concave curved surface and the radius of curvature R of the convex curved surface are each a radius of curvature of an arc on a cross section as taken along a plane including a center axis of the tire, and characterized in that when N1 represents a distance, in the radial direction, to an end of each turned-up portion of the carcass ply from a bead base line that passes through a lower end of the core and is parallel to the center axis of the tire, a ratio N1/R of the distance N1 in the radial direction to the radius of curvature R of the convex curved surface, satisfies 2.1 ≤ N 1 / R ≤ 3.5. a tread having an outer surface that forms a tread surface; a pair of sidewalls that extends almost inward, in a radial direction, from ends, respectively, of the tread; a pair of beads positioned almost inward of the sidewalls, respectively, in the radial direction; a clinch portion that extends from the sidewalls to the beads, and a carcass ply that is extended, along the tread and the sidewalls, on and between both the beads, wherein each bead includes a core and a bead apex positioned outward of the core in the radial direction, the carcass ply includes a main body portion and turned-up portions which are formed by the carcass ply being turned up from an inner side toward an outer side around the core, and a concave curved surface extends on an outer surface of the clinch portion in a circumferential direction, and the concave curved surface is engageable with a convex curved surface formed on an outer side end, in the radial direction, of a rim flange, a ratio R1/R of a radius of curvature R1 of the concave curved surface to a radius of curvature R of the convex curved surface of the rim flange, satisfies 1.7 ≤ R 1 / R ≤ 2.5, and the radius of curvature R1 of the concave curved surface and the radius of curvature R of the convex curved surface are each a radius of curvature of an arc on a cross section as taken along a plane including a center axis of the tire, and