This invention relates to apparatus for moistening and conditioning sheet materials for example leathers and similar materials. The apparatus comprises two endless moisture-absorbent conveyor belts which come together, in the operation of the apparatus, between a pair of opposed flat presser surfaces. The apparatus comprises means for moistening the conveyor belts and for heating at least one of the flat surfaces. The apparatus also comprises means for moving the flat surfaces apart to permit introduction of material carried between the conveyor belts into the region between the flat surfaces and together to press the material on the belt. By reason of this pressure an intensive heat transfer occurs from the flat surfaces to the conveyor belt whereby the water in the conveyor belt is evaporated and transferred into the leather. The apparatus further comprises drive means whereby the belts are moved to transport the leather or other sheet material only while the flat surfaces are spaced apart.