A blood pump (1; 201; 301), comprising: - a pump casing (2; 202; 302) having a blood flow inlet (21; 221; 321) and a blood flow outlet (22; 222; 322), - an impeller (3; 203; 303) arranged in said pump casing (2; 202; 302) so as to be rotatable about an axis of rotation for conveying blood from the blood flow inlet (21; 221; 321) to the blood flow outlet (22; 222; 322), and - an outflow cannula (4; 204; 304) having an upstream end portion (41; 241; 341), a downstream end portion (43; 243; 343) and an intermediate portion (42; 242; 343) extending between the upstream end portion (41; 241; 341) and the downstream end portion (43; 243; 343), the upstream end portion (41; 241; 341) of the outflow cannula (4; 204; 304) being connected to the pump casing (2; 202; 302) such that blood is conveyed from the blood flow outlet (22; 222; 322) of the pump casing (2; 202; 302) into and through the intermediate portion (42; 242; 342) of the outflow cannula (4; 204; 304) towards the downstream end portion (43; 243; 343) of the outflow cannula (4; 204; 304), wherein the downstream end portion (43; 243; 343) has a blood flow outlet (44; 244; 344) through which blood can exit the outflow cannula (4; 204; 304) and which is arranged at least partially radially inwards relative to an outermost circumference of the outflow cannula's intermediate portion (42; 242; 342), wherein at least a portion of the intermediate portion (42; 242; 342) of the outflow cannula (4; 204; 304) has an outer diameter that is larger than an outer diameter of the pump casing (2; 202; 302), characterized in that at least the outflow cannula's intermediate portion (42; 242; 342) is sized and shaped to contact an inner wall of a patient's vessel (104; 108) in which the blood pump (1; 201; 301) is placed during operation of the blood pump (1; 201; 301), in order to occlude the vessel (104; 108) during operation of the blood pump. - a pump casing (2; 202; 302) having a blood flow inlet (21; 221; 321) and a blood flow outlet (22; 222; 322), - an impeller (3; 203; 303) arranged in said pump casing (2; 202; 302) so as to be rotatable about an axis of rotation for conveying blood from the blood flow inlet (21; 221; 321) to the blood flow outlet (22; 222; 322), and - an outflow cannula (4; 204; 304) having an upstream end portion (41; 241; 341), a downstream end portion (43; 243; 343) and an intermediate portion (42; 242; 343) extending between the upstream end portion (41; 241; 341) and the downstream end portion (43; 243; 343), the upstream end portion (41; 241; 341) of the outflow cannula (4; 204; 304) being connected to the pump casing (2; 202; 302) such that blood is conveyed from the blood flow outlet (22; 222; 322) of the pump casing (2; 202; 302) into and through the intermediate portion (42; 242; 342) of the outflow cannula (4; 204; 304) towards the downstream end portion (43; 243; 343) of the outflow cannula (4; 204; 304), wherein the downstream end portion (43; 243; 343) has a blood flow outlet (44; 244; 344) through which blood can exit the outflow cannula (4; 204; 304) and which is arranged at least partially radially inwards relative to an outermost circumference of the outflow cannula's intermediate portion (42; 242; 342), wherein at least a portion of the intermediate portion (42; 242; 342) of the outflow cannula (4; 204; 304) has an outer diameter that is larger than an outer diameter of the pump casing (2; 202; 302),