A reinforcing concrete pier comprising a concrete member 1a, and structural main reinforcing bars 1b embedded in the concrete member so as to extend along an axial direction of the concrete member. A high-strength core member 2, which is higher in strength than the structural main reinforcing bars, is embedded in the concrete member inside the structural main reinforcing bars so as to extend along the axial direction. One end portion 2b with a gap of the core member is fixed to the concrete member at a base portion of the pier, and the other end portion 2a of the core member is fixed to the concrete member at an intermediate portion 1d of the pier. Further, the core member has an unbounded region D in which the core member is not bonded to the concrete member between the one end portion and the other end portion.