Disclosed is a pneumatic run-flat radial tire of side reinforcing type, which has significantly improved run-flat durability without adversely affecting actual vehicle properties such as ride comfort.The pneumatic run-flat radial tire includes a carcass layer 5, a main belt 8, a tread portion 9, a side wall portion 12, and a reinforcing rubber layer 13 having a substantially crescent cross section. A cord having a difference in thermal shrinkage stress between at 30° C. and at 80° C. of 3.0×10−2 cN/dtex or more is used as cords of at least one carcass ply of the carcass layer 5. The slope a of decreasing rate (%) of the dynamic storage modulus of elasticity E′ of the reinforcing rubber 13 from 30° C. to 50° C. satisfies the following condition: α≦−3.0×10−2[%]/[deg]; and the slope β of decreasing rate (%) of the dynamic storage modulus of elasticity E′ from 50° C. to 80° C. satisfies the following condition: β≧−8.0×10−2[%]/[deg].