An absorbent structure and method for making the absorbent structure including an absorbent core made from a matrix of fibers, wherein the matrix is reinforced with a stretchable reinforcing member, such as scrim. The absorbent matrix may be secured to the web of scrim with the scrim in a stretched condition. When the web of scrim is in an unstretched condition, the web of scrim partially gathers the absorbent core to form rugosities on the core. The reinforcing member can have a non-uniform transverse width to conform to the shape of the absorbent core. The absorbent structure can have multiple layers of reinforcing members. The reinforcing member has strands arranged in a pattern to facilitate stretching. A first set of strands can cross a second set of strands at junction in a non-orthogonal relationship.