A power transmission shaft having an improved strength and ensuring a stable torsion fatigue strength. The power transmission shaft has coupling members respectively provided on the opposite ends of an pipe part made of a steel material. The steel material includes 0.30-0.45% by weight of C, 0.05-0.35% by weight of Si, 1.0-2.0% by weight of Mn, 0.05% by weight or less of Al, 0.01% by weight or less of S, and the remainder (iron Fe and unavoidable impurities). The pipe part has an electro-unite portion that extends in the axial direction. The electro-unite portion and neighborhood thereof are hardened so as to have a Rockwell hardness HRC of 45 or more. Also, another power transmission shaft has coupling members integrally formed on opposite ends thereof. In addition, the shaft is formed from a steel element tube by a plastic working. The shaft has an inner diametrical surface which is subjected to a high-frequency induction hardening and tempering treatment to make the surface portion hardness of the inner diametrical surface to have a Rockwell hardness HRC of 35 or more.