The document discusses stretchable nonwoven fabrics. While nonwovens are inexpensive, flexible and disposable, they lack aesthetics, drape, softness and elasticity. A stretchable nonwoven is created using an elastic core component such as thermoplastic polyurethane surrounded by an extensible sheath fiber to provide processability and haptics. Air or electrostatic power is used to separate the core-sheath fibers which are then collected onto a perforated film to form a stretchable nonwoven web. These composite elastic nonwovens have high absorption, a soft feel, can be easily fitted to desired shapes and resemble knitted fabrics. They have applications in medical materials, baby clothes,