A tubular member is manufactured by continuously supplying a plurality of elongate flexible webs (U,X,Y,Z) while transversely disaligning side edges of the webs, such that the webs are arranged in echelon, progressively wrapping the webs around a mandrel (M), bonding the webs with adhesive layers interposed therebetween to form a tubular member, and joining the displaced side edges to complete the tubular member. The webs are supplied in mutually spaced-apart relation under longitudinal tension. A plurality of resilient support plate members (3) are disposed respectively for the webs and arranged to lie along the lower surfaces of the webs transversely thereof. Opposite ends (19,20) of the support plate members are supported for movement vertically and toward and away from each other. The opposite ends of the support plate members are movable towards each other to curve the support members along an outer peripheral surface of the mandrel (M). A positioning device has a pair of guide members (4,5) mounted on an inner surface of each of the support plate members for engaging opposite side edges of one of the webs.