PURPOSE: To enable a mirror surface finish to be easily performed on a soft metal, by using a water permeable disc-shaped polishing tool, having a polishing grain in size of 10μm or less, and polishing the metal in a predetermined feed speed.

CONSTITUTION: A disc-type polishing tool 1 mounts to its polishing action surface a water permeable polishing material 6 adhesively attaching a polishing grain in size of 10μm or less. When assumed Dmm for diameter of said polishing action surface, NTrpm for rotary speed of the tool 1, Vfmm/min for relative feed speed of the tool 1 for a work 7 and PwKgf/cm2 for pressing pressure of the tool 1 for the work 7, polishing is performed while supplying machining fluid into the tool 1 to be allowed to flow out from jetting ports 5 under the condition of an expression I in the drawing. In this way, a mirror surface finish is performed into surface roughness of about 0.02μm on a surface of the work consisting of soft metal of aluminum, copper, etc.