Bioprocess bags are provided which retain good mechanical characteristics after radiation sterilization. The bags are constructed from a copolymer of tetrafluoroethylene. The tetrafluoroethylene is polymerized with at least one monomer selected from the group consisting of: ethylene; chlorotrifluoroethylene; vinyl fluoride; hexafluoropropylene; hexafluoroisobutene; monomers represented by CH2═CX1(CF2)nX2 (wherein X1 is H or F, X2 is H, F, or Cl, and n is an integer of 1 to 20); perfluoro(alkyl vinyl ethers) represented by CF2═CF—ORf1 (wherein Rf1 is a C1-C20 perfluoroalkyl group or a C1-C17 perfluoroalkoxy alkyl group); and alkyl perfluorovinyl ether derivatives represented by CF2═CF—OCH2—Rf2 (wherein Rf2 is a C1-C5 perfluoroalkyl group). A particular version is polymerized with ethylene and CH2═CX1(CF2)nX2 (wherein X1 is H or F, X2 is H, F, or Cl, and n is an integer of 1 to 20). Various versions of the bag have high resistance to repeated bending, folding, and creasing; low water vapor transmissibility; high puncture resistance; high biocompatibility; and low reactivity. This makes them suitable for storing biomaterials and medical materials.