An apparatus for sorting and stacking thin rigid plates, such as used in storage batteries, receives the plates horizontally in spaced-apart groups, transports the groups horizontally and deposits them into stacks on a stacking apparatus that orients them vertically and delivers them for further processing. The groups of plates are carried on a conveyor system having chains that are spaced further apart than the width of the plates. Opposed pads extending inwardly from the chains engage the edges of the plates. Each pad has a length approximately equal to the height of the plates and is separated from each adjacent pad by a distance that is greater than the height of the plates. Stops located between the chains contact the groups of plates and prevent their continued movement with the chains thus causing them to drop between adjacent pads and off of the conveyor. In a preferred embodiment the apparatus includes a collection system that causes every group of plates in a stack to drop the same distance. Also, in a preferred embodiment, at least some groups of plates in each stack are displaced onto a transfer conveyor, that operates at a lower speed than the main conveyor, before they reach the stacking apparatus. Thus, there is more time between the arrival of groups of plates at the stacking apparatus, which permits the just formed stack to be advanced without interference from the first group of the next stack.