Process for manufacturing a plastic-based cellular structure comprising: a step (a) during which parallel lamellae of a composition based on at least one thermoplastic polymer (P) chosen from amorphous and semi-crystalline polymers are continuously extruded through a die containing a plurality of parallel slots; a step (b) during which, on exiting the die and in successive alternations, the spaces between two adjacent lamellae are subjected to an injection of a fluid (f) and to a vacuum, the two sides of a same lamella being, for one side, subjected to the action of the fluid (f) and, for the other side, to the action of the vacuum, and inversely during the following alternation, in order to produce deformation of the lamellae and to weld them in pairs with formation, in a plane approximately parallel to the extrusion direction, of a cellular structure whose constituent cells extend perpendicular to the extrusion direction; a step (c) during which the cellular structure obtained in step (b) is drawn perpendicular to the extrusion direction.