An implantable controllable fluid flow valve structure for location within an anatomical tube such as a vein or artery, or between apertures in the walls of a vein and artery, is described. The structure has a relatively rigid tubular housing 1 with a tubular elastic cylindrical member 2 within it where the ends of the cylindrical member 2 are attached to the interior wall of the tubular housing 1. The space between the housing wall and the elastic cylindrical member can be increased, for example by pumping fluid 8 under pressure into it, which causes the elastic cylindrical member 2 to distend and thus reduce the flow cross-section of the valve. Mechanical means may be used to effect such distention. The valve structure is particularly useful for use as a valve to control flow through an arteriovenous fistula made surgically, and can also be used as an artificial sphincter.