Method for producing a planar resilient composite material which has a carrier layer of a resilient material, in particular in the form of a textile material, and a cover layer of wood veneer which is connected to said carrier layer and is more rigid in comparison to the latter, wherein a structure (26, 260) configured in the form of a plurality of grooves (265a, 265b, 265c, 265d) is engraved in the wood veneer of the cover layer by means of laser engraving, so as to increase the resilience of the wood veneer of the cover layer, comprising the following method steps: - establishing the structure (26, 260) to be engraved in the wood veneer of the cover layer, and importing the structure (26, 260) into a control apparatus of a laser engraving device specified in programming terms; - arranging the composite material on a worktable of the laser engraving device in such a manner that the wood veneer of the cover layer of the composite material is located on the side facing away from the worktable; and - activating at least one laser head (18, 183a, 183b) of the laser engraving device that is connected to the control apparatus, and engraving the structure (26, 260) in the wood veneer of the cover layer of the composite material by means of the laser beam (181a, 181b) generated by the laser head (18, 183a, 183b), characterized in that at least two laser heads (183a, 183b) of the laser engraving device that are connected to the control apparatus are activated so as to, by means of the laser beam (181a, 181b) of a respective laser head (183a, 183b), engrave the structure (26, 260) simultaneously in adjacent regions (B1, B2) of the wood veneer of the cover layer of the composite material that are assigned to a respective laser head (183a, 183b), wherein the laser heads (18, 183a, 183b) in programming terms are controlled in such a manner that in a fist overlapping portion of the adjacent regions (B1, B2) of the composite material the structure (26, 260) is engraved in the wood veneer of the cover layer randomly in part by the laser beam (181a, 181b) of the one laser head (183a, 183b) and in part by the laser beam (181a, 181b) of the other laser head (183a, 183b). - establishing the structure (26, 260) to be engraved in the wood veneer of the cover layer, and importing the structure (26, 260) into a control apparatus of a laser engraving device specified in programming terms; - arranging the composite material on a worktable of the laser engraving device in such a manner that the wood veneer of the cover layer of the composite material is located on the side facing away from the worktable; and - activating at least one laser head (18, 183a, 183b) of the laser engraving device that is connected to the control apparatus, and engraving the structure (26, 260) in the wood veneer of the cover layer of the composite material by means of the laser beam (181a, 181b) generated by the laser head (18, 183a, 183b), characterized in that at least two laser heads (183a, 183b) of the laser engraving device that are connected to the control apparatus are activated so as to, by means of the laser beam (181a, 181b) of a respective laser head (183a, 183b), engrave the structure (26, 260) simultaneously in adjacent regions (B1, B2) of the wood veneer of the cover layer of the composite material that are assigned to a respective laser head (183a, 183b), wherein the laser heads (18, 183a, 183b) in programming terms are controlled in such a manner that in a fist overlapping portion of the adjacent regions (B1, B2) of the composite material the structure (26, 260) is engraved in the wood veneer of the cover layer randomly in part by the laser beam (181a, 181b) of the one laser head (183a, 183b) and in part by the laser beam (181a, 181b) of the other laser head (183a, 183b).