A multipipe heat exchanger for use in extracorporeal circulation of blood, comprising: a heat exchanger case;; a plurality of heat transfer pipes loaded in inside of said heat exchanger case a heat exchange medium inlet port having a shape of a straight pipe, attached to an outer surface on a one end side of said heat exchanger case such that an extension of a pipe axis crosses a cylinder axis of said heat exchanger case and said extension extends toward the other end side of said heat transfer pipe, and supplying a prescribed heat exchange medium to an outer surface of said heat transfer pipe; and a heat exchange medium outlet port attached to said outer surface of said heat exchanger case, on a side opposite in a direction of cylinder diameter of said heat exchanger case to a position where said heat exchange medium inlet port is attached, for discharging said heat exchange medium supplied to said outer surface of said heat transfer pipe, said plurality of heat transfer pipes in a bundled state having a circumferential portion arranged at a short distance from an inner surface of said heat exchanger case and a first bowstring-shaped portion which retracts toward a center in the direction of cylinder diameter from an arc formed by said circumferential portion, and said plurality of heat transfer pipes in the bundled state being loaded in said inside of said heat exchanger case such that said first bowstring-shaped portion and said inner surface of said heat exchanger case on a side where said heat exchange medium inlet port is attached are opposed to each other characterized in that said inner surface of said heat exchanger case on the side where said heat exchange medium inlet port is attached is formed substantially in such a tapered shape as gradually protruding toward the center in the direction of cylinder diameter such that a distance (H72L) between said inner surface and said first bowstring-shaped portion becomes gradually smaller from said one end side of said heat exchanger case toward the other end side of said heat exchanger case. a heat exchanger case;; a plurality of heat transfer pipes loaded in inside of said heat exchanger case a heat exchange medium inlet port having a shape of a straight pipe, attached to an outer surface on a one end side of said heat exchanger case such that an extension of a pipe axis crosses a cylinder axis of said heat exchanger case and said extension extends toward the other end side of said heat transfer pipe, and supplying a prescribed heat exchange medium to an outer surface of said heat transfer pipe; and a heat exchange medium outlet port attached to said outer surface of said heat exchanger case, on a side opposite in a direction of cylinder diameter of said heat exchanger case to a position where said heat exchange medium inlet port is attached, for discharging said heat exchange medium supplied to said outer surface of said heat transfer pipe,; a plurality of heat transfer pipes loaded in inside of said heat exchanger case a heat exchange medium inlet port having a shape of a straight pipe, attached to an outer surface on a one end side of said heat exchanger case such that an extension of a pipe axis crosses a cylinder axis of said heat exchanger case and said extension extends toward the other end side of said heat transfer pipe, and supplying a prescribed heat exchange medium to an outer surface of said heat transfer pipe; and a heat exchange medium outlet port attached to said outer surface of said heat exchanger case, on a side opposite in a direction of cylinder diameter of said heat exchanger case to a position where said heat exchange medium inlet port is attached, for discharging said heat exchange medium supplied to said outer surface of said heat transfer pipe, said plurality of heat transfer pipes in a bundled state having a circumferential portion arranged at a short distance from an inner surface of said heat exchanger case and a first bowstring-shaped portion which retracts toward a center in the direction of cylinder diameter from an arc formed by said circumferential portion, and said plurality of heat transfer pipes in the bundled state being loaded in said inside of said heat exchanger case such that said first bowstring-shaped portion and said inner surface of said heat exchanger case on a side where said heat exchange medium inlet port is attached are opposed to each other characterized in that said inner surface of said heat exchanger case on the side where said heat exchange medium inlet port is attached is formed substantially in such a tapered shape as gradually protruding toward the center in the direction of cylinder diameter such that a distance (H72L) between said inner surface and said first bowstring-shaped portion becomes gradually smaller from said one end side of said heat exchanger case toward the other end side of said heat exchanger case.