Abstract: As a laminated film formed by continuously melt extruding an .alpha.-olefin polymer as a covering film on a traveling, continuous substrate film of an .alpha.-olefin polymer is being cooled by means of a cooling roll contacting the covering film side, pressing rolls are pressed against the laminated film on the substrate film side, along the lateral edge parts thereof, and toward the cooling roll thereby to cause local plastic deformation and thinning of the cover film, which has not fully solidified, due to elastic deflection without appreciably thinning the substrate film, and then the pressing rolls are retracted away from the laminated film, whereby thin-film regions for ensuring positive gripping by tentering clips for lateral stretching are formed along the lateral edge parts.