A pneumatic tire for travelling over rough terrain, having a pair of bead portions, sidewall portions respectively continuous with the bead portions and extending in the tire radial direction, and a tread portion continuous with the respective sidewall portions, wherein: the tire has a plurality of fin-like projections provided in the tire circumferential direction with intervals therebetween in an outer surface of the sidewall portion such that the fin-like projections each protrude from the outer surface and extend in the tire radial direction; each fin-like projection has an end portion on the inner side in the tire radial direction and an end portion in the outer side in the tire radial direction, and a surface of at least the end portion on the outer side in the tire radial direction is formed to have an arcuate configuration protruding toward the tire inner surface side in a cross section in the width direction of the tire; the arcuate surface of the end portion on the outer side in the tire radial direction of the fin-like projection is smoothly connected to an outer side surface of a shoulder block provided on the outermost side in the tire width direction of the tread portion; an annularly protruding side portion is provided in a region, adjacent to the shoulder block, of the outer surface of the sidewall such that the annularly protruding side portion protrudes from the outer surface, and the respective end portions on the outer side in the tire radial direction of the fin-like projections are linked by the annularly protruding side portion; characterized in that: the pneumatic tire is a motorcycle tire; provided that h represents the maximum protruding height, along a line normal to the outer surface of the sidewall portion, of the fin-like projection, p represents a pitch at which the fin-like projections are provided in the tire circumferential direction and w represents the maximum width in the tire circumferential direction of the fin-like projection, 1 ≤ p/h ≤ 20 and 2w ≤ p ≤ 51w; and each fin-like projection extends from the inner end portion in the tire radial direction of the shoulder block toward a rim line position by a length equivalent to at least 30 % of the length along the tire radial direction of the sidewall portion in a state where the tire has been assembled with a prescribed rim and inflated at the normal internal pressure. the tire has a plurality of fin-like projections provided in the tire circumferential direction with intervals therebetween in an outer surface of the sidewall portion such that the fin-like projections each protrude from the outer surface and extend in the tire radial direction; each fin-like projection has an end portion on the inner side in the tire radial direction and an end portion in the outer side in the tire radial direction, and a surface of at least the end portion on the outer side in the tire radial direction is formed to have an arcuate configuration protruding toward the tire inner surface side in a cross section in the width direction of the tire; the arcuate surface of the end portion on the outer side in the tire radial direction of the fin-like projection is smoothly connected to an outer side surface of a shoulder block provided on the outermost side in the tire width direction of the tread portion; an annularly protruding side portion is provided in a region, adjacent to the shoulder block, of the outer surface of the sidewall such that the annularly protruding side portion protrudes from the outer surface, and the respective end portions on the outer side in the tire radial direction of the fin-like projections are linked by the annularly protruding side portion; characterized in that: the pneumatic tire is a motorcycle tire; provided that h represents the maximum protruding height, along a line normal to the outer surface of the sidewall portion, of the fin-like projection, p represents a pitch at which the fin-like projections are provided in the tire circumferential direction and w represents the maximum width in the tire circumferential direction of the fin-like projection, 1 ≤ p/h ≤ 20 and 2w ≤ p ≤ 51w; and each fin-like projection extends from the inner end portion in the tire radial direction of the shoulder block toward a rim line position by a length equivalent to at least 30 % of the length along the tire radial direction of the sidewall portion in a state where the tire has been assembled with a prescribed rim and inflated at the normal internal pressure. the pneumatic tire is a motorcycle tire; provided that h represents the maximum protruding height, along a line normal to the outer surface of the sidewall portion, of the fin-like projection, p represents a pitch at which the fin-like projections are provided in the tire circumferential direction and w represents the maximum width in the tire circumferential direction of the fin-like projection, 1 ≤ p/h ≤ 20 and 2w ≤ p ≤ 51w; and each fin-like projection extends from the inner end portion in the tire radial direction of the shoulder block toward a rim line position by a length equivalent to at least 30 % of the length along the tire radial direction of the sidewall portion in a state where the tire has been assembled with a prescribed rim and inflated at the normal internal pressure.