Abstract: Apparatus for cutting by a high pressure fluid jet comprising a working nozzle supplying a fluid jet, a worktable able to support a material to be cut, a mechanism for displacing the working nozzle in a given cutting direction and a jet recovery system, wherein the worktable has a slot facing the working nozzle in the cutting direction, the jet recovery system being positioned behind said slot and having a chute at the bottom in which circulates a relatively cold liquid, an alveolar material placed at the inlet to the chute and set back relative to the worktable, and a vacuum is provided at the inlet to the chute, between the worktable and the alveolar material. Application to the cutting of materials in sheet form, as well as composite materials.