Disclosed is a non-nested, two-ply, absorbent fibrous sheet material consisting of two webs which each have a plurality of crests and depressions on its surface facing the other web. The crests on each web are positioned between the crests of the other web and are spaced from the depressions of the other web to leave spaces in the sheet material for increased absorbency and bulk. The two webs are joined together at locations intermediate the crests and depressions of at least one of the webs, preferably by mechanical welding in a manner which produces perforations in the sheet material. Also disclosed is the method and apparatus for making the two-ply sheet material.