A bag assembly (1) comprises a backing component (2) and affixed thereto a plastics bag (3) for receiving and holding a container of a liquid sample (particularly a container holding a specimen of a liquid body fluid such as blood, urine, or sputum to be sent to a laboratory for analysis. The plastics bag (3) is formed from two sheets of liquid impervious plastics material (9, 10) bonded together to form the bag (3) and leave a mouth therefor and contains a pad (4) of absorbent material. The bag assembly may be produced by a method which comprises the steps of: (a) advancing a web (203) of a backing component, (b) laying onto the advancing web (203) of the backing component an advancing first web (205) of a liquid impervious plastics material and bonding the webs (203 and 205) together along a join line (204), (c) depositing pads of absorbent material (4) at intervals onto the exposed surface of the advancing first plastics web (205), (d) laying advancing second web of liquid impervious plastics material (207) onto the first web of plastics material (205) so as to sandwich the absorbent pads (4) between the first and second plastics webs (205, 207), (e) bonding said first and second plastics webs (205, 207) together along a line extending transversely of the plastics webs between successive absorbent pads, and (f) severing the web produced in step (e) along said first transverse lines.