A filter device has a filter housing and a round filter element received in the interior of the filter housing. The round filter element has a filter medium body with a wall flowed through radially relative to a longitudinal axis of the filter medium body by a fluid to be purified. The round filter element has a first end disk and a second end disk arranged at opposed end faces of the filter medium body. The filter medium body has an inwardly positioned flow space inside the filter medium body that is the raw side of the round filter element. A support grid is arranged externally at the wall of the filter medium body. The filter housing has a housing cover with a flow guiding rib arranged at an inner side of the housing cover facing the interior. The flow guiding rib projects into the inwardly positioned flow space.