The present invention relates to a method for producing a web of an elastic non-wovencomposite material (24) comprising the following steps: Feeding and deliveringa first non-woven layer (4, 4a) in a longitudinal direction (L) feeding a pluralityof elastic filaments (6) connecting the plurality of elastic filaments (6)to a first side (70) of the non-woven layer (4, 4a) to form a composite material(14) at least in some regions overstretching of the first non-woven layer (4,4a) in the longitudinal direction (L) by feeding the composite material (14)through the gap of a pair of profiled, intermeshing stretching rollers (15),by which the composite material (14) is stretched in the longitudinal direction(L), wherein the elastic filaments (6) are arranged in the non-woven compositematerial such that they are substantially oriented in the longitudinal direction(L), so that they have at most 10 intersecting points with each other per cm
