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. The second ply will, upon stretching of the laminate, be at least to a degree permanently elongated so that, upon release of the applied tensile forces, it will not return to its original undistorted configuration. This results in z-direction bulking of the laminate web when the applied tension is released as well as elastic extensibility in the direction of initial stretching, at least up to the point of initial stretching. In a particularly preferred embodiment of the present invention, the mechanical stretching of said laminate web is carried out by passing said laminate web between at least one pair of meshing corrugated rolls, the degree of meshing between said corrugated rolls being non-uniform about the periphery of said rolls, whereby said laminate web is subjected to non-uniform incremental stretching as it passes therebetween to produce a varying degree of elasticity in the resultant web.