An intravascular blood pump for percutaneous insertion comprises a catheter (10) and a pumping device (1) attached to the catheter (10). The catheter (10) extends along a longitudinal axis and has a distal end (11) and a proximal end (12) opposite the distal end (11). The catheter (10) comprises an elongate stiffening structure (15) extending continuously longitudinally along the length of the catheter (10) between the proximal end (11) and the distal end (12) of the catheter (10). The stiffening structure (15) may comprise a shape-memory material, such as Nitinol. It may be in the form of a wire that extends loosely through the lumen of the catheter and helps to avoid or significantly reduce kinks in the catheter.