In order to manufacture a sausage skein of any geometrical external contour, a sausage-forming device has a coextrusion head for coextruding a paste mass and a casing enclosing the mass, wherein the extrusion head is provided with a filling tube for ejecting the paste mass and an extrusion die assigned to the filling tube with an extrusion gap for the casing material, wherein the filling tube exhibits, at least in the region of the ejection end, a cross-sectional shape deviating from the circular shape and the extrusion gap exhibits a cross-sectional shape deviating from the annular ring.