An air-bearing center-guiding apparatus 10 and a method are disclosed for supporting and laterally center-guiding thin flexible webs of paper or plastic under 15 mils in thickness. The apparatus comprises a web support and guide member 22 having an inner surface and an outer web-facing surface. Parallel rows of elongated spaced-apart guide apertures 34 extend longitudinally along edge regions of the web. Each guide aperture 34 is formed from a cylindrical opening in the web support and guide member 22 and extends substantially perpendicular to the web. Within each aperture a flat-sided dowel 60 is mounted to define a flow passage shaped in cross-section like a segment of a circle 62. Each circular-segment guide aperture 34 has a straight side 54 and a curved side 52 for directing a jet of air against the web edge 56. A plurality of the circular-segment guide apertures 34 develop a guiding force for holding lateral movement of the web to plus or minus 0.001 inch (0.0254 mm). A row of web-support apertures 32, separate from the guide apertures 34, is provided between the rows of guide apertures 34 to form an air bearing for supporting the web.