A pump device (1) for administering a medical fluid to a patient comprises a holding device (10) for receiving a syringe barrel (20) of a syringe (2), the holding device (10) comprising a stationary section (101) and a holding member (11) movable with respect to the stationary section (101) between an opened position and a closed position, wherein the holding member (11) is configured to secure, in the closed position, the syringe barrel (20) of a syringe (2) received on the holding device (10) with respect to the stationary section (101). A shaft (130) is coupled to the holding member (11), the shaft (130) being constituted to rotate during a movement of the holding member (11). Herein, a damping device (14) comprises a movable part (140) connected to the shaft (130) and rotatable together with the shaft (130) and a stationary part (141) fixed with respect to the stationary section (101) of the holding device (10), a rotational movement of the movable part (140) with respect to the stationary part (141) providing for a damping of the movement of the holding member (11). In this way a pump device for administering a medical fluid to a patient is provided which may provide for a secure fastening of a syringe barrel and at the same time helps to avoid a damaging of in particular smaller syringes by clamping forces of the holding member.