Blood is separated by filtration through a filter medium (11) of pore size less than 3 microns, mounted in a dividing wall (5), between two halves (6 and 7) of a flexible bag (1). The filter medium is sandwiched between pre and post filters of pore size 8 to 100 microns. Flexible inlet (8) and outlet (9) tubes enter either end of the bag. An Independent claim is given for an arrangement of a number of filter bags for the separation of whole blood into its components as it is collected from the donor.