A filter unit (10) and a filter device formed from several such units for filtering a fluid, especially a process fluid such as required for chip-removing machining processes. The filter units (10) each comprise a frame (11) and a filter medium (16). The frame (11) has support webs (12), which reinforce the frame (11) and support the filter medium (16). The support webs (12) are arranged on the downstream side (18) of the filter medium (16) to prevent clogging on the upstream side (17) and permit a simple removal of the filter cake. The filter units (10) are stacked on each other in alternating orientation such that the upstream sides (17) or the downstream sides (18) of two adjacent individual filter units (10) face each other. The frame (11) forms unfiltered fluid and filtered fluid flow nozzles (13), (14) through which the fluid to be filtered or the filtered fluid can flow.