The invention concerns an alveolar structure (1) comprising at least one alveolar zone (2a, 2b) partially delimited by an associated leak tight surface (4a, 4b) . According to the invention, each alveolar zone (2a, 2b) is formed of a plurality of metallic layers (8) superimposed parallel to the associated leak tight surface (4a, 4b), each metallic layer (8) comprising a network of passages (10) opening out on either side of said metallic layer (8).The invention further concerns a method for manufacturing said alveolar structure (1)Application to fuel cells and heat exchangers.