An apparatus for manufacturing cellular laminate structural panels includes one or more supply stations (62) of a flexible strip material (96) including folding rollers (66) for sequentially folding the strip material into cellular structures and feeding the cellular structures into a conveyor where the cellular structures are held in compression. The apparatus further includes a laminating station (68) where the folded cellular structures are laminated to an upper and/or lower sheet material to which lines of a bonding medium (74) have been applied prior to engagement with the cellular structures. The folded cellular structures are heated (176) before engaging the sheet material so as to enhance the bonding of the sheet material to the cellular structures and subsequent to bonding, the laminate is passed through a cooling station (227) to set the bonding medium. Downstream from the laminating station, the laminate passes through a side edge folding station (80) where edges of the sheet material are folded over side edges of the laminate to finish the side edges of the laminate and subsequently the laminate is passed into a cutter (82) for cutting the continuous laminate into predetermined lengths. Ends of the cut panels then receive rigid edge strips (86) to fully finish the panel. The method of the invention includes the steps performed by the components of the apparatus.