In the slitting of a web of material such as aluminum by passage of the web over at least one pair of symmetrically-arranged circular knives and respective counterknives to excise a narrow waste strip from two between newly formed sub-webs, the improvement which comprises temporarily and elastically deforming said circular knives over a portion of their peripheries downstream of their points of cut whereby said knives at such portions will be prevented from contacting the edges of said subwebs. To this end, in an apparatus as described a pair of rotatable wheels are resiliently urged against said circular knives just downstream of the points where the knives disengage the counterknives.