An automatically cleanable milk filter for filtering milk that is obtained in a milking device for milking dairy animals, and comprising a cylindrical housing with a longitudinal direction and with a cylindrical outer wall, a first end with a first liquid connection, and a second end with a second liquid connection, wherein, during use of the filter, the second end is situated above the first end, wherein a substantially concentric cylindrical filter part containing a plurality of filter openings with a smallest diameter of between 60 and 100 μm and a cylindrical core which is placed concentrically within the filter part are accommodated in the housing, which filter part comprises wire with a unilaterally tapering cross-sectional profile and a frame, which wire is provided in a spiral shape with a plurality of windings or in a series of individual parallel rings or rods, wherein the frame is configured to keep the windings or the rings or the rods at a mutual distance, as a result of which the plurality of filter openings is provided between the windings or the rings or the rods, wherein the filter part divides the filter volume into a first volume part which is directly connected to the first liquid connection, and a second volume part which is directly connected to the second liquid connection, wherein the second volume part comprises a cylindrical part, as well as a top part which narrows at a transition to the second liquid connection, wherein said cylindrical part, viewed in a direction towards the second liquid connection, extends at least a predetermined distance beyond the plurality of filter openings in the filter part, and wherein said first volume part, viewed in a direction towards the second liquid connection, does not extend beyond the filter part, in particular up to a highest filter opening. and comprising a cylindrical housing with a longitudinal direction and with a cylindrical outer wall, a first end with a first liquid connection, and a second end with a second liquid connection, wherein, during use of the filter, the second end is situated above the first end, wherein a substantially concentric cylindrical filter part containing a plurality of filter openings with a smallest diameter of between 60 and 100 μm and a cylindrical core which is placed concentrically within the filter part are accommodated in the housing, which filter part comprises wire with a unilaterally tapering cross-sectional profile and a frame, which wire is provided in a spiral shape with a plurality of windings or in a series of individual parallel rings or rods, wherein the frame is configured to keep the windings or the rings or the rods at a mutual distance, as a result of which the plurality of filter openings is provided between the windings or the rings or the rods, wherein the filter part divides the filter volume into a first volume part which is directly connected to the first liquid connection, and a second volume part which is directly connected to the second liquid connection, wherein the second volume part comprises a cylindrical part, as well as a top part which narrows at a transition to the second liquid connection, wherein said cylindrical part, viewed in a direction towards the second liquid connection, extends at least a predetermined distance beyond the plurality of filter openings in the filter part, and wherein said first volume part, viewed in a direction towards the second liquid connection, does not extend beyond the filter part, in particular up to a highest filter opening.