The invention involves a rotary anode of an x-ray tube with a cooling element of carbon fiber material constructed so as to be rotationally symmetrical around a coaxial rotation axis. In order to achieve a high heat conducting capability, it is recommended that the base of the cooling element (14) be a preform constructed according to the tailored fiber placement process (TFP), that the cooling element have a hollow cylinder and a one-piece construction, that the carbon fibers (22) run parallel along its entire length or basically parallel to the axis (16) and have a heat conductivity .lamda. with .lamda.>/=250 W/m.times.K, and that the carbon fibers be connected across a matrix containing carbon whose graphite crystallites are aligned along the carbon fibers.