The grader and/or sorter consists of a conveyor (1) with a series of cups (3) hinged along their front edges (11) and tipping when actuated by a control unit to discharge the fruit onto a transverse removal conveyor. Each cup is equipped with a flap (17) of a flexible material that trails behind it and lessens the impact of the fruit as it is tipped from the cup onto a chute (27) leading to the removal conveyor.