Abstract: A method for producing a planar resilient composite material which has a carrier layer of a textile material and a cover layer of wood veneer which is connected to the carrier layer. A groove structure is engraved in the wood veneer of the cover layer via laser engraving. The structure to be engraved is established and imported into a control apparatus of a laser engraving device, the composite material is placed on a worktable, and a laser head connected to the control apparatus is activated so as to engrave the structure in the wood veneer of the cover layer. At least two laser heads of the laser engraving device are activated so as to, via the laser beam of a respective laser head, engrave the structure simultaneously in adjacent regions of the wood veneer of the cover layer of the composite material that are assigned to a respective laser head.