A method of and apparatus for feeding a continuous thin film plastic tape or like, pliable, foldable strip in an oscillatory fashion, which may be random, from a feed surface having a width many times greater than the width of said tape to a receiving surface having a width at least as great as a tape width and many times narrower than the width of the feed surface by spacing and positioning the feed and receiving surfaces with respect to one another to limit the maximum angle between a transverse plane bisecting the receiving surface and extending towards the approaching tape and the centerline of the tape. The maximum value of this angle, in degrees, is about 6.5 times the inverse of the tape width expressed in inches. The invention is illustrated with an apparatus which converts the oscillatory motion of a tape fed from a roll many times wider than the tape over an equally large roller surface to a pulley only slightly wider than the tape and many times smaller than the roller surface.