A non-invasive arterial blood pressure monitor uses an inflatable cuff that incorporates the first bladder that is filled with non-compressible liquid or gel. The bladder can be pressurized by an action of a pressurizing device superimposed onto its outer surface. In a preferred embodiment, a pressurizing device is an air-filled second bladder being connected to an air pump and bleed valve. The first bladder is positioned between the patients body and the second bladder. During operation, the second bladder compresses the first bladder, which, in turn, compresses the patients artery against the supporting bone. The mechanical coupling between the blood-filled artery of a patient and the liquid-filled bladder of a dual-bladder cuff is improved for detecting pressure oscillations in a broad frequency range. The pressure sensor that is coupled to the first bladder also functions as a hydrophone for picking-up the mechanical oscillations from any part of the occluded limb or digit. This allows for improved computation of the arterial pressure.