Apparatus for collating and stacking building components, for example tiles, has pairs of conveyors with shelves for supporting edges of tiles. The tiles are fed to the shelves by a conveyor and the pairs of conveyors move upwardly in timed relation to locate tiles on the shelves. When all the shelves are full, the pairs of conveyors move downwards and apart to deposit the tiles in a stack on to a support. The timing of this avoids shock loads on the tiles. The stack of components is then banded and removed from the apparatus.