It is very common to have an itchy stubble at first when you decide to grow a beard. When you shave, you leave a sharp edge to each hair follicle and once it starts growing, the tougher bristles of the hair scrape against the edges of the follicle - this is what causes an itchy stubble.
FULLY GROWN BEARDS
If you’ve got a full beard and it’s feeling itchy, this may be caused by the dry skin under beard. Facial hair removes the moisture from the skin, drawing it up from the surface and onto the hairs, where it quickly evaporates. This can leave the skin extremely dry or flaky and even cause beard dandruff. Also, dead skin cells that usually get removed by daily face washing or exfoliating get stuck in the hair, and the dirt and oil build-up can cause skin irritation.