A method for making a composite tubular structure, such as the inner skin of an acoustic liner, includes providing a tool that is adjustable between a molding position and a non-molding position. The tool has a base on which are mounted a plurality of sectors, each sector having an outer panel provided with a predetermined shaped surface. The predetermined shaped surface corresponds to a portion of the contour of the tubular structure to be formed. At least one of the sectors is fixed relative to the base while the remaining sectors are movable in a radial direction and separable from all the other sectors. The method includes adjusting the movable sectors until the tool is in the molding position, applying composite material on an outer surface of each sector, curing the composite material to form an inner skin, and removing the inner skin from the outer surface. The thus-formed composite tubular structure may be remounted on the tool for bonding to additional exterior layers.