The invention concerns a method of handling stacks of flexible substrates (14) by means of a gripper (8) as well as a robot cell (1) for carrying out the method. The gripper (8) is arranged on an arm (6) of a robot (2) and has a lower finger and a corresponding upper finger. The method comprises the steps of inserting said lower finger below a bottom substrate (14) of a stack resting on a base and said upper finger above a top substrate (14) of the stack, and gripping the stack by clamping it between said lower and upper finger. Then by means of the gripper (8) starting at a stack front the entire stack is lifted into a pendent state and moved to a support (16). There the stack is lowered such that a stack rear, which is opposite to said stack front, comes into contact with the support (16). Finally the entire stack is laid out on the support (16) with said bottom substrate (14) up by further lowering and while horizontally displacing the gripper (8) in a bottom-to-top substrate direction before letting the gripper (8) release the stack.