A milking device for milking a dairy animal, and provided with - milking means, - a control unit for the milking device, - a milk line (5-1, 5-2, 5-3) for transporting the milk from the milking means to a milk tank, - a milk filter for filtering the milk passing through the milk line, and - a cleaning device for cleaning the milk filter with cleaning liquid (42, 43), wherein the milk filter comprises: - a housing which surrounds a filter volume (22, 24), and which comprises a milk inlet part with a milk inlet, a milk outlet part with a milk outlet, and a circumferential outer wall in between, - a filter component which is provided in the filter volume and comprises a circumferential plate part comprising a plurality of filter holes, and which divides the filter volume into a central inner filter volume which is connected to one of the milk inlet and the milk outlet, and an outer filter volume surrounding the latter, and connected to the other one of the milk inlet and the milk outlet, characterised in that the milk filter is configured to be flushed, in use, in a first direction with the milk to be filtered, which first direction runs from the milk inlet to the milk outlet, wherein the cleaning device is configured to clean the milk filter by passing cleaning liquid (42, 43) through the milk filter in a countercurrent direction opposite to the first direction in at least two consecutive pulses, in such a way that in every pulse: - during a first pulse stage, more cleaning liquid is supplied than is discharged, and - subsequently, during a second pulse stage, at least as much cleaning liquid flows from the filter volume as is supplied, so that an amount of cleaning liquid collected in the filter volume up to a liquid level (h 1) which surrounds at least a portion of the plurality of holes. - milking means, - a control unit for the milking device, - a milk line (5-1, 5-2, 5-3) for transporting the milk from the milking means to a milk tank, - a milk filter for filtering the milk passing through the milk line, and - a cleaning device for cleaning the milk filter with cleaning liquid (42, 43), wherein the milk filter comprises: - a housing which surrounds a filter volume (22, 24), and which comprises a milk inlet part with a milk inlet, a milk outlet part with a milk outlet, and a circumferential outer wall in between, - a filter component which is provided in the filter volume and comprises a circumferential plate part comprising a plurality of filter holes, and which divides the filter volume into a central inner filter volume which is connected to one of the milk inlet and the milk outlet, and an outer filter volume surrounding the latter, and connected to the other one of the milk inlet and the milk outlet, - a housing which surrounds a filter volume (22, 24), and which comprises a milk inlet part with a milk inlet, a milk outlet part with a milk outlet, and a circumferential outer wall in between, - a filter component which is provided in the filter volume and comprises a circumferential plate part comprising a plurality of filter holes, and which divides the filter volume into a central inner filter volume which is connected to one of the milk inlet and the milk outlet, and an outer filter volume surrounding the latter, and connected to the other one of the milk inlet and the milk outlet, characterised in that the milk filter is configured to be flushed, in use, in a first direction with the milk to be filtered, which first direction runs from the milk inlet to the milk outlet, wherein the cleaning device is configured to clean the milk filter by passing cleaning liquid (42, 43) through the milk filter in a countercurrent direction opposite to the first direction in at least two consecutive pulses, in such a way that in every pulse: - during a first pulse stage, more cleaning liquid is supplied than is discharged, and - subsequently, during a second pulse stage, at least as much cleaning liquid flows from the filter volume as is supplied, so that an amount of cleaning liquid collected in the filter volume up to a liquid level (h 1) which surrounds at least a portion of the plurality of holes. - during a first pulse stage, more cleaning liquid is supplied than is discharged, and - subsequently, during a second pulse stage, at least as much cleaning liquid flows from the filter volume as is supplied, so that an amount of cleaning liquid collected in the filter volume up to a liquid level (h 1) which surrounds at least a portion of the plurality of holes.