A process and machine for manufacturing a tubular element, for example for use in forming boxes, in which a strip of material is wound around a mandrel having a cross-section corresponding to that of the tubular element to be formed. The strip of material is arranged to extend in a plane and the mandrel is applied against the strip in a direction perpendicular to said plane to cause lateral parts of the strip to lift up on either side of the mandrel and to define two flaps projecting above the mandrel. A force is then exerted on each of the flaps in a direction parallel to said plane to fold the flaps down onto the mandrel and to bring their free edges into abutment.