A method for priming a blood processing filter (1A, 1B) comprising a sheet-like filter element, and a flexible container having an internal space that is divided into one side and another side by the filter element, the flexible container comprising: a first container forming part and a second container forming part that are arranged opposite each other so as to sandwich the filter element therebetween, an inlet port that is provided in the first container forming part and that serves as an inlet for blood, an outlet port that is provided in the second container forming part and that serves as an outlet for blood, a band-shaped annular first seal part that seals the first container forming part and the filter element and that is formed so as to surround the inlet port, and an annular second seal part that seals at least the first container forming part and the second container forming part and that is formed so as to surround the first seal part along an outer edge of the second container forming part; wherein: the first container forming part has an interior filtration space forming part and an exterior surrounding space forming part that are separated by the first seal part, and the second container forming part has an extension space forming part that is surrounded by the second seal part and is arranged opposite the filter element and the surrounding space forming part; and the inlet port is provided in the filtration space forming part and communicates with an internal space on the one side that is defined by the filter element, and the outlet port is provided in the extension space forming part and communicates with an internal space on the other side that is defined by the filter element and protrudes further than an outer surface of the extension space forming part; the method being characterized in that the extension space forming part is not divided by the first seal part, and by turning the blood processing filter (1A, 1B) sideways with the outlet port facing downwards, and setting the blood processing filter (1A, 1B) on a mounting face in a state in which blood processing filter (1A, 1B) is inclined with respect to the mounting face; and filling a priming fluid from the outlet port of the blood processing filter (1A, 1B) that is set on the mounting face to remove air from inside the blood processing filter (1A, 1B). the first container forming part has an interior filtration space forming part and an exterior surrounding space forming part that are separated by the first seal part, and the second container forming part has an extension space forming part that is surrounded by the second seal part and is arranged opposite the filter element and the surrounding space forming part; and the inlet port is provided in the filtration space forming part and communicates with an internal space on the one side that is defined by the filter element, and the outlet port is provided in the extension space forming part and communicates with an internal space on the other side that is defined by the filter element and protrudes further than an outer surface of the extension space forming part; the method being characterized in that the extension space forming part is not divided by the first seal part, and by turning the blood processing filter (1A, 1B) sideways with the outlet port facing downwards, and setting the blood processing filter (1A, 1B) on a mounting face in a state in which blood processing filter (1A, 1B) is inclined with respect to the mounting face; and filling a priming fluid from the outlet port of the blood processing filter (1A, 1B) that is set on the mounting face to remove air from inside the blood processing filter (1A, 1B).