Disclosed is a method and apparatus, associated with a rotary transfer device having a plurality of radially extending circumferentially spaced arms, for flattening and maintaining thermoplastic web segments or bags in a flat condition at a pick-up or transfer station so that successive segments or bags are being engaged and transferred by the arms of the transfer device are free of folds or wrinkles and thus insure proper stacking on one or more upwardly extending posts at a stacking station.