Abstract: A multilayer bag structure having at least two laminated layers, the innermost layer being composed of a random copolymer of ethylene and an alpha-olefin having 5 to 10 carbon atoms, said copolymer having the following characteristics: (1) it has an ethylene content of 99.5 to 94 mole %, (2) it has a melt index at 190.degree. C. of 0.1 to 20, (3) it has a density of 0.915 to 0.940 g/cm.sup.3, (4) it has a p-xylene-soluble content (A) at 25.degree. C. of 0.5 to 5% by weight, (5) it has a boiling n-heptane-insoluble content (B) of not less than 8% by weight to less than 20% by weight, and (6) the total of (A) and (B) is not more than 20% by weight.