In a fluid polishing method for processing a fine aperture by slurry 7, the slurry is supplied from a cylinder 2a in a slurry flow rate target process until the flow rate increases to a target value of a slurry feed flow rate. When the flow rate reaches the target flow-rate, the cylinder is stopped and switched to another cylinder 2b and the operation fluid flow rate of the fine aperture is thereafter measured. In a metering process, to be executed next, a necessary processing time is calculated on the basis of the operation fluid flow rate and polishing is carried out for a necessary processing time by another cylinder 2b. Another cylinder is then stopped and switched and the operation fluid flow rate is measured. In this way, the metering process is repeated until the operation fluid flow rate reaches a predetermined value. In each process, the supply of the slurry is not interrupted.