The men forced their way into the flat in Burns Court, Kirkintilloch, and threatened the 64-year-old woman and her 45-year-old son with a weapon.
The mother was not injured but her son was seriously assaulted and suffered cuts to his head.
He was treated at Glasgow Royal Infirmary before being released.
Police are hunting the two attackers and have been carrying out door-to-door inquiries.
The first man is described as about 6ft 2ins and in his early 30s with a heavy build. The second attacker is younger and described as "podgy".
Anyone with information is asked to call police on 101.