A method of measurement and analysis of supra-systolic blood pressure waveforms obtained non-invasively from a brachial artery in an arm of a patient, using a blood pressure cuff pressure transducer, to estimate central artery blood pressures, said method comprising the steps of: (a) inflating the blood pressure cuff on the patient's arm to a supra-systolic pressure; (b) measuring a succession of cuff pressure waveforms associated with the brachial artery representing at least one cardiac ejection cycle with cuff pressure transducer; (c) analyzing the measured cuff pressure waveforms using a mathematical model relating the heart-pulse synchronous cuff pressure signal and brachial pressure near the cuff to produce an estimated brachial pressure signal and pressure waveforms, wherein the model comprises scaling the cuff pressure signal relative to previously measured systolic and diastolic pressures, such that the amplitude of the estimated brachial pressure signal is a proportion of the difference between measured systolic and diastolic pressures; (d) analyzing the estimated brachial pressure waveforms using a mathematical model for relating the estimated brachial pressure signal and a central pressure at the root of the brachial artery to produce estimated central artery blood pressures and estimated central blood pressure waveforms, wherein this mathematical model includes as parameters: i) an impedance relationship at the blood pressure cuff, which is a reflection coefficient; and ii) a parameter relating a phase of the pressure wave at substantially the subclavian root to a phase of a supra-systolic pressure wave at the occluding cuff, which is a propagation time; and wherein the parameters are estimated based on previously measured data, characteristics of the patient and/or measurements taken from the subject; and (e) generating an output representing the estimated central artery pressures and pressure waveforms based on the analysis. (a) inflating the blood pressure cuff on the patient's arm to a supra-systolic pressure; (b) measuring a succession of cuff pressure waveforms associated with the brachial artery representing at least one cardiac ejection cycle with cuff pressure transducer; (c) analyzing the measured cuff pressure waveforms using a mathematical model relating the heart-pulse synchronous cuff pressure signal and brachial pressure near the cuff to produce an estimated brachial pressure signal and pressure waveforms, wherein the model comprises scaling the cuff pressure signal relative to previously measured systolic and diastolic pressures, such that the amplitude of the estimated brachial pressure signal is a proportion of the difference between measured systolic and diastolic pressures; (d) analyzing the estimated brachial pressure waveforms using a mathematical model for relating the estimated brachial pressure signal and a central pressure at the root of the brachial artery to produce estimated central artery blood pressures and estimated central blood pressure waveforms, wherein this mathematical model includes as parameters: i) an impedance relationship at the blood pressure cuff, which is a reflection coefficient; and ii) a parameter relating a phase of the pressure wave at substantially the subclavian root to a phase of a supra-systolic pressure wave at the occluding cuff, which is a propagation time; and wherein the parameters are estimated based on previously measured data, characteristics of the patient and/or measurements taken from the subject; and i) an impedance relationship at the blood pressure cuff, which is a reflection coefficient; and ii) a parameter relating a phase of the pressure wave at substantially the subclavian root to a phase of a supra-systolic pressure wave at the occluding cuff, which is a propagation time; and wherein the parameters are estimated based on previously measured data, characteristics of the patient and/or measurements taken from the subject; and (e) generating an output representing the estimated central artery pressures and pressure waveforms based on the analysis.