A gripping device for gripping an egg tray (3A) having a dimpled structure includes a gripping unit (4) that is movable up and down to engage and grip the egg tray (3A) and move it. The gripping unit comprises (4) at least a pair of opposite gripping members (42A, 42B) which are movable in opposite directions, substantially transverse to the up and down movement of the unit (4), from a retracted position to an advanced position to grip a dimple (31) of the egg tray (3A), and from the advanced position to the retracted position to release the dimple. Each gripping member (42A, 42B) of said pair has a separate pressure operated actuator (46) operatively connected to it. The actuator (46), upon pressurization, moves the corresponding gripping member (42A, 42B) from the retracted position to the advanced position.