Abstract: A "zero strain" stretch laminate web exhibiting a non-uniform degree of elasticity, as measured in the direction of elasticization at various points along an axis oriented substantially perpendicular to the direction of elasticization. Improved method and apparatus for non-uniformly stretching "zero strain" stretch laminate webs to impart elasticity thereto in the direction of stretching, at least up to the point of initial stretching are also disclosed. The "zero strain" stretch laminate material is formed of at least two plies of material which are either intermittently or substantially continuously secured to one another along at least a portion of their coextensive surfaces while in a substantially untensioned ("zero strain") condition. One of the plies is stretchable and elastomeric, while the second ply is elongatable, but not necessarily elastomeric.