A method and a device (09) for cutting and folding a fabric section (34) from a continuous material sheeting (01) for producing multilayer casings, in particular pillowcases, having a first gripper (25) that secures and pulls off the front edge (31) of the material sheeting (01) by a first partial amount. A second gripper (26) secures the material sheeting (01) behind the front edge (31) to form a folded edge (33), which can be pulled off by a second partial amount, and at the same time, folded together in multiple layers by movement of the second gripper (26) combined with resetting of the first gripper (25), and a cutting device (27) cuts the material sheeting (01) to form the fabric section (34) the length of which between the front edge (31) and the rear edge (36) corresponds to the sum of the first and second partial amounts.