A lid is provided for covering or sealing a cup by engaging a rim flange of the cup. The lid includes a top portion and an annular side plate which extends downwardly from periphery of the top portion. The plate is formed with a hole. An engagement plate is disposed on the side plate. A bottom edge of the engagement plate is connected to the plate. A top edge of the engagement plate stretches upwardly along the hole, so that the engagement plate is located in the hole. The plates are flexible. As such, the engagement plate can be pressed and bent inwardly when the lid covers a cup. The engagement plate would then engage with the rim flange of the cup so as to enhance engagement of the lid and the cup.