A web processing apparatus has a cutting mechanism for cutting elongate webs of different widths from a raw web, a core rotating mechanism for selectively holding cores having different diameters and different axial lengths and rotating a selected one of the cores in opposite directions, a winding mechanism for supporting one of the elongate webs on an outer circumferential surface of the core to wind the elongate web in different winding directions when the core is rotated, and a cutting mechanism for cutting an end of the elongate web to produce a roll after the elongate web is wound around the core.