To accomplish a web transfer, which in reliability is comparable to the one obtained with a closed draw, in any operating environment, but especially where it is desirable to transfer a fast running tissue web (4) from the drying section of a tissue machine, e.g., a Yankee dryer (2), to a reel-up (3), a web support device (10) extends across the width of the web (4) and along a predetermined run of the web support device has a support surface (11) formed by a series of plate member assemblies (23) having means for creating a flow of air in the direction of the web run. Between the web (4) and the support surface (11) the flow of air forms an air layer (15) of reduced static pressure, so as to stabilize the web (4) against flutter. The predetermined run may extend through a calender (7) and past scanner equipment (8). Pneumatic tail threading capabilities may be included.