A food supplement material, and method of its preparation, containing ellagic acid (i.e., in the form of bio-available ellagitannins) and also containing the so-called punicosides (i.e., punicalagins A and B), is derived from pomegranate plant materials. Most preferably, the food supplement is extracted from pomegranate seed (although the whole fruit or any part thereof, as well as pomegranate leaves, may be used), and contains from about 5% to about 90% ellagic acid (ellagitannins), and is presented for human oral administration as a dry powder contained in gelatin capsules, soft gel capsules, or tablet form for daily consumption. The food supplement inherently also contains the so-called punicosides.