A non-invasive sensor has a contact membrane (6,16) and a cover membrane (2,12), the cover membrane being adapted for extension of a body surface to project the contact membrane against a body surface beneath it. The contact membrane will normally be attached to the cover membrane around its periphery such that at least one of the membranes forms a convex outer surface, and a spacing material (8,20) can be interposed between the membranes to achieve this object. The cover membrane may extend over a support element (10), with the contact membrane overlaying and spaced from the other face of the support element by spacing material.