Cryopreservation container of animal cell

A combination of a cryopreservation container and an enclosure container in which an animal cell to be frozen and preserved is enclosed together with a cryopreservation medium, said combination comprising:

• a cryopreservation container comprising a bottomed hollow container body, said container body including an inner wall portion having an open top forming a hollow container portion, an outer wall portion surrounding said inner wall portion, and a hollow heat conductivity-retarded liquid portion between said inner wall portion and said outer wall portion, a lid for closing said hollow container portion, and heat conductivity-retarded liquid enclosed within said hollow heat conductivity-retarded liquid portion of said container body, wherein said heat conductivity-retarded liquid comprises a liquid which provides, when ambient temperature of the cryopreservation container is -60.degree. C..about.-100.degree. C., a cooling rate in said container body of -0.5.degree. C./min..about.-2.degree. C./min;
• and
• an enclosure container for enclosing an animal cell to be frozen and preserved together with a cryopreservation medium.