A number of properties of polygranular carbon bodies can be improved by small quantities of carbon fibers being incorporated in the formulations for production of such bodies. However, it has proven difficult for carbon fibers to be introduced into the green mixture. Therefore, a high-grade coke, preferably needle coke, in accordance with the invention is used to produce the polygranular carbon bodies. This high-grade coke according to the invention contains the carbon fibers simply as a result of being produced in the delayed coker of a refinery. All the main details of the way in which a coke of this type is mixed into the green mixture correspond to the reliably managed processing of other needle cokes.