A laminate of thermoplastic polymeric films comprises at least one fluted ply A and at least one substantially flat ply B, adhered to one another in bonded zones along the flute crests. The wavelength of the flutes is preferably no more than 3 mm. Ply A has a generally uniform thickness or can have attenuated zones of lessor thickness extending parallel to the flute direction, each bonded zone being located mainly within an attenuated zone. The flutes can be sinuous with crests on both sides of ply A and can be adhered on each side to a ply B, in which case, attenuated zones can be on both sides and can have different widths. The flutes can be filled with filler material, including reinforcement strands, and one or both sides can be perforated. The method and apparatus employ aligned grooved fluting rollers and a grooved laminating roller.