Here we use 2-D models of fluid film lubrication and contact mechanics to calculate the contact stress and fluid (i.e., slurry) pressure distributions on the wafer–pad interface in CMP. In particular, the effective rigidity of the wafer (determined by the wafer carrier structure), the retaining ring width and its back pressure are taken to be the design parameters. The purpose is to study the synergetic effects of such parameters on the contact stress non-uniformity (NU), which directly affects the spatial non-uniformity of the material removal rate on the wafer surface. Our numerical results indicate that, for a given wafer rigidity, one may choose a particular combination of the retaining ring parameters to minimize NU. Also, the corresponding minimum NU decreases with the effective wafer rigidity, suggesting that it is beneficial to use a soft (e.g., floating-type) wafer carrier. Moreover, for a soft wafer carrier, the presence of the retaining ring also reduces NU to some extent, but the use of a multi-zone wafer-back pressure profile would be more effective in this regard.