While running in the hole with 7” casing, joint #6 was picked up and moved to the floor using a sling.  The Floorman hooked up the casing elevator and installed the safety pin. Thereafter the Floorman signaled to the driller to lower the winch line. While waiting the Floorman put his left hand between the elevator and bail eye. As the winch was lowered his Left Hand index finger was crushed resulting in damage to his finger and nail bed.