A method for processing semiconductor wafers, which provides planarized surface in a well controllable manner and with high accuracy by processing a film with uneven surface, formed over a semiconductor wafer, within the area of a working surface with a diameter larger than that of said semiconductor wafer by not more than two times, and by processing the film with a polishing liquid supplied from a supply unit disposed on a vertically arranged working surface is disclosed. Additionally, high quality dressing of the working surface can be easily performed by virtue of the smaller diameter of the working surface. Furthermore, the vertical arrangement of the working surface makes possible ready compatibility with semiconductor wafers of enlarged diameters.