An apparatus for additive manufacturing of three-dimensional objects by successive, selective layer-by-layer exposure and thus successive, selective layer-by-layer solidification of construction material layers of construction material that can be solidified by means of an energy beam, comprising a filter device provided for filtering process gas arising in the course of performing additive construction processes in a process chamber of the apparatus, wherein the filter device comprises several filter modules with a filter module housing each, wherein every filter module housing comprises a filter body receiving room configured with a defined geometry provided for receiving a defined number of filter bodies configured with a defined geometry, wherein every filter module comprises connection interfaces on the filter module via which it is or can be connected, if required, to defined connection areas of a pipe structure of the apparatus that is or can be flown through by the process gas.