Abstract: A completely dry fluid-tight reciprocating vacuum pump comprises one or more pumping chambers defined between two rigid parts which face one another in the axial direction. One is reciprocated in a straight line relative to the other. They are connected to one another by at least one axially flexible member of appropriate radial stiffness. Each of these members comprises an outside part fixed to a first of these rigid parts. The side of the first rigid part facing the flexible member is shaped to have a profile in diametral cross-section which is substantially the same as the profile in diametral cross-section that this member tends to assume, by virtue of its stiffness, in the configuration with the aforementioned rigid parts moved towards one another. The pump can be used for pumping corrosive and radioactive gases, such as tritium, for example.