Abstract: A process and apparatus for stacking layers of composite material on moulding equipment comprises a transfer band on which each of two opposed working sections has a surface suction device to hold on it a layer that has been placed in a precise position in register with an outline, projected onto the transfer band by means of neon tubes and a frosted glass plate in a first working station. The band transfers the layer to a second working station where the layer is isolated in a sealed enclosure by means of an inflatable joint carried by a frame facing a peripheral ridge surrounding the moulding equipment. Reduced pressure is produced in the enclosure via a reduced pressure outlet causing the transfer band to be displaced towards the moulding equipment and draping the layer over the latter.