Abstract: Apparatus is disclosed for non-invasively monitoring a subject's blood pressure, in which a flexible diaphragm that encloses a fluid-filled chamber is compressed against tissue overlying an artery, with sufficient force to compress the artery. A first, relatively slow servo control system optimizes the amount of artery compression, which occurs at a mean transmural pressure of about zero, by modulating the volume of fluid within the chamber and noting the resulting effect on the pressure within the chamber. Since different pressure effects are realized according to the amount of artery compression, an appropriate control signal can be produced that provides the optimum mean diaphragm pressure. In addition, a second, relatively fast servo control system supplies the fluid to and from the chamber, so as to compensate for pressure variations within artery.