A lack of knowledge about the construction of tight packing is now the main obstacle for a successful design of artificial proteins. In this paper we examine a way of close packing antiparallel beta-sandwiches. We show that there are some 'weak points' at the surfaces of beta-sheets, which cannot be filled by the surrounding aliphatic side chains that are the most abundant. Theoretically, these 'weak points' can be filled either by aromatic side chains of the same sheet or by the residues of the other parts of the protein molecule. The analysis of protein structures shows that both possibilities are used by nature and that there are many cases when these 'weak points' are not filled by any atom. They remain free and form a majority of the defects of close packing in protein globules.