We consider the following generalization of graph packing. Let and be graphs of order and a bipartite graph. A bijection from onto is a list packing of the triple if implies and for all , . We extend the classical results of Sauer and Spencer and Bollobás and Eldridge on packing of graphs with small sizes or maximum degrees to the setting of list packing. In particular, we extend the well-known Bollobás–Eldridge Theorem, proving that if , and , then either packs or is one of 7 possible exceptions.