PCT No. PCT/JP96/00041 Sec. 371 Date Sep. 16, 1997 Sec. 102(e) Date Sep. 16, 1997 PCT Filed Jan. 12, 1996 PCT Pub. No. WO96/21760 PCT Pub. Date Jul. 18, 1996A composite elastic material comprises a non-woven fabric secured to an elastic member. The non-woven fabric is elastically stretchable by about 100% or more. The sheet-like elastic member has an elastic recovery of about 60% or more and a break-down elasticity of about 200% or more. The elastic member and the non-woven fabric are secured together at a plurality of points in the stretchable direction of the non-woven fabric. The composite elastic material has multiple-stage elongation characteristics including a first stress lowering point caused by changes in the structure of the non-woven fabric, and a second stress lowering point occurring at an elongation larger than that of the first stress lowering point, caused by the fracturing of the sheet-like elastic member. The elastic material clearly shows a break-down point when stretched, and increases the flexibility of designing various products.