A pump apparatus (1) comprises a pump head (2) and a container (20) for a liquid to be dispensed. The pump head (2) has a flexible dispensing tube (4) in fluid connection with the inside of the container (20). The fluid connection between the dispensing tube (4) and the inside of the container (20) is provided by a supply tube (28) which co-operates with the dispensing tube (4) to provide a non-return valve function. An end (48) of the supply tube (28) is disposed within an end of the dispensing tube (4) and the non-return valve function is provided by a hole (46) through a side wall of the supply tube (28) in a region where the dispensing tube (4) overlaps the supply tube, whereby the dispensing tube (4) provides a seal over the hole (46) to prevent ingress of fluid when the internal pressure is lower than the external pressure. Another aspect of the invention provides a container (20) for use in the pump apparatus.
