Traditional cuffs for measuring blood pressure use an air chamber enclosed in a non-stretchable fabric to occlude an artery in a limb when supplied with pressurised air. A stethoscope used on the limb is used to monitor blood flow. Application of the cuff is inconvenient and correct placement of the stethoscope chestpiece requires skill. According to the invention blood pressure measurement is facilitated by having the air chamber enclosed in a pre-formed shell-like structure being flexible around the limb and stiff along the limb and by using a linear array of microphones to detect the blood flow noises, the best signal from one of the microphones being automatically selected. Furthermore, the invention provides a facility for correcting the reading in dependence of the amount of wrap of the limb.