An improved method and apparatus for incrementally stretching "zero strain" stretch laminate webs to impart elasticity thereto in the direction of initial stretching, at least up to the point of initial stretching. 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 subsequent 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 opposed peripheral edge portions of the laminate web to be incrementally stretched are subjected to restraint to substantially prevent inwardly directed slippage or contraction thereof in a direction parallel to the direction of stretching. This maximizes the effectiveness of the incremental web stretching operation by forcing the "zero strain" stretch laminate web to undergo the fullest possible degree of elongation during the incremental stretching operation.