An apparatus for planarizing semiconductor wafers in its preferred form includes a rotatable platen for polishing a surface of the semiconductor wafer and a motor for rotating the platen. A non-circular pad is mounted atop the platen to engage and polish the surface of the semiconductor wafer. A polishing head holds the surface of the semiconductor wafer in juxtaposition relative to the non-circular pad. A polishing head displacement mechanism moves the polishing head and semiconductor wafer across and past a peripheral edge of the non-circular pad to effectuate a uniform polish of the semiconductor wafer surface. Also disclosed is a method for planarizing a semiconductor surface using a non-circular polishing pad.