A physics-based mathematical model is used to estimate central pressure waveforms from measurements of a brachial pressure waveform measured using a supra-systolic cuff. The method has been tested in numerous subjects undergoing cardiac catheterisation. Central pressure agreement was within 11 mm Hg and as good as the published non-invasive blood pressure agreement between the oscillometric device in use and the so-called “gold standard.” It also exceeds international standards for the performance of non-invasive blood pressure measurement devices. The method has a number of advantages including simplicity of application, fast calculation and accuracy of prediction. Additionally, model parameters have physical meaning and can therefore be tuned to individual subjects. Accurate estimation of central waveforms also allow continuous measurement (with intermittent calibration) using other non-invasive sensing systems including photoplethysmography.