The invention relates to a pump device (100) for pumping a fluid. The pump device (100) comprises a substrate layer (102) and a polymer layer (104) which has a polymer layer recess (108) in a rest position. Additionally or alternatively, the substrate layer (102) has a substrate layer recess (106). Depending on the embodiment, the substrate layer (102) covers the polymer layer recess (108) and / or the polymer layer (104) fluid-tightly covers the substrate layer recess (106) to form a fluid channel (110) for transporting the fluid (112). The pumping device (100) is further provided with an activation unit (114) configured to change a shape of the polymer layer (104) such that a cross section of the fluid channel (110) is reduced.
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