A device for forming envelopes from a continuous flat strip of a sleeve-like foil material, comprising a supply member, a cutting member for making a cut over the full width of the material so as to provide individual envelopes, and a discharge member for discharging the envelopes. The cutting member comprises at least two cutting elements movable relative to the strip of material, each cutting element comprising at least one cutting blade extending parallel to the width of the strip, such that the individual cutting blades form several partial cuts contiguous to each other in the foil material over the width thereof in successive cutting operations.