Apparatus (100) for stacking bales of hay into large bundles, for example, three bales high and seven bales wide, positions bands (44) about the stacked array to provide a tightly bound, compressed stack of bales. The stacking apparatus (100) compresses the stacked bales during banding with a greater force applied to the same facing portions of the bales as applied during formation of the bales to form a solid, self-supporting large bundle made up of smaller bales. The apparatus is computer controlled and fully automated from the input of individual bales to the discharge of a tightly banded and compressed bundle (80) of hay bales and can be used while traversing a field containing the individual hay bales (51).