A process for overwrapping a catamenial device such as a tampon includes the steps of providing a substantially cylindrical overwrapper material, inserting a catamenial device into the overwrap material, and closing the open end of the overwrapper material. The overwrapper material has an open end, a closed end, and a first length. The catamenial device has a tapered insertion end, a longitudinal axis, and a length less than the first length, such that the open end of the overwrapper material extends beyond the insertion end of the inserted catamenial device. Concave clamping jaws are applied to the open end of the overwrapper material to urge it toward the longitudinal axis of the catamenial device; to conform portions of the overwrapper material to the insertion end of the catamenial device; and to fold overwrapper material between adjacent clamping jaws to form fins extending outwardly from the conformed portions.