The present invention provides a rubber composition for a sidewall, which improves fuel economy, handling stability, tensile strength at break, elongation at break, and processability in a balanced manner, and which can also suppress the occurrence of broken spews during demolding of a resulting tire; and a pneumatic tire formed from the rubber composition. The present invention relates to a rubber composition for a sidewall, comprising a rubber component having: a combined amount of a 1,2-syndiotactic polybutadiene crystal-containing butadiene rubber and a butadiene rubber synthesized in the presence of a rare earth catalyst of 5 to 60% by mass; an amount of a terminally modified butadiene rubber of 7 to 60% by mass; and an amount of an isoprene-based rubber of 20 to 70% by mass, each based on 100% by mass of the rubber component, wherein the rubber composition has: a combined amount of a carbon black having a nitrogen adsorption specific surface area of 25 to 120 m2/g and a silica having a nitrogen adsorption specific surface area of 70 to 250 m2/g of 20 to 40 parts by mass; and an amount of zinc oxide of 3.6 to 16 parts by mass, each per 100 parts by mass of the rubber component.