In this paper, the with-in-wafer non-uniformity (WIWNU) of the lager quadrate optic in the fast polishing process (FPP) is discussed from the machine side. At the machine side, the non-uniform stress on the wafer surface is the major reason for the non-uniform material removal rate which results in the WIWNU. Stresses arise mainly from two sources, namely the pressure exerted by the polishing pad and shear stress due to the relative motion between the wafer and pad. Based on the special chemical mechanical polishing FPP, the kinematic motion of the wafer is analyzed and the non-uniform stress is analyzed by a 3D axisymmetric quasi-static model. The WIWNU can be reduced by adjusting the stress.