A material is provided that is particularly suited for use in absorbent articles. The material has a base layer of a generally non-elastic material and at least two strips or regions of elastomeric material attached to the base layer material with a space therebetween such that a center region of the base layer material is bordered on at least two sides by composite regions of the elastomeric materials and the base layer material. The center region of base layer material remains generally non-extensible and the composite regions are stretchable in at least a first direction as a result of tensioning and necking-in the base layer material prior to attaching the elastomeric materials. The invention includes methods for making the material, as well as absorbent articles incorporating the materials.