The apparatus comprises a housing (12) defining one or more treatment cells (14, 16, 18) having a sheet material path (20) extending therethrough from an entrance (22) to an exit (24). The entrance (22) and exit (24) are each closed by a respective drive roller (26) in contact with a reaction surface (28, 50) to define a nip (29) therebetween through which the sheet material path (20) extends. Rotatable sealing means (30) seal each drive roller (26) to the housing (12). A reduced pressure is established within the treatment cell (14, 16, 18). The continuous treatment of sheet materials can be carried out under reduced pressure, in a convenient and reliable manner.