In a filter apparatus 1, a central filter rod 6 is arranged in the interior 14 of a filter housing 2, the diameter d of which filter rod tapers in the direction of flow of the plastic melt. On the filter rod 6 are arranged filter discs 7 which are parallel to one another and have outer and inner diameters of equal size. The filter apparatus 1 operates as a continuous-flow filter apparatus in which the plastic melt flows in via an intake 4 and flows out via an outlet 5. A filter housing wall inner surface 3 tapers in the direction of flow of the plastic melt, so that a gap width h.sub.a (x) between a filter disc outer rim 8 and the filter housing wall inner surface 3 decreases in the direction of flow of the plastic melt.