A method for manufacturing a heat and material exchange apparatus comprising a plurality of columns and by a series of at least three metal plates of rectangular section, the plates being substantially all of the same shape and dimensions, each plate being separated from the adjacent plate by a group of hollow metal columns that are aligned and have a section which is polygonal, the columns of each group being parallel to one another, the columns of each group each being in contact with the two metal plates on either side of the group, at least some of the columns of a group containing a material and heat exchange means, at least the parts of the plates which are in contact with the columns being coated with a brazing material wherein the plates are secured to the columns by placing the exchange apparatus in a furnace and by heating the furnace in order to braze the apparatus to form a parallelepipedal block.