Disposable garments such as disposable diapers are disclosed that possess improved elastic characteristics. At least one garment outer sheet is composed of a drawable fabric, such as melt blown polymeric fibers or melt spun filaments. An elastic element is affixed in the relaxed condition to a web of outer sheet fabric. The elastic web is then stetched, and simultaneously the web in the area of elastic element attachment is drawn to impart a molecular orientation to the web fibers. As a result, the web fibers are permanently elongated. Upon relaxation of the stretched elastic element, shirrs or gathers are formed in the web fibers that permit subsequent stretching of the elastic element when the garment is worn. One of the outside sheet webs need not be drawable or drawn if it is preformed with corrugations or pleats in the region of elastic element attachment. The present invention also includes apparatus for manufacturing the garment. The apparatus includes novel rolls for pre-corrugating one garment sheet and for simultaneously stretching the elastic element and drawing the web in the region of elastic element attachment. Alternately, the entire web may be drawn, rather than just in the region of elastic element attachment.