In chemical mechanical planarization, a rotating wafer is pressed facedown against a rotating pad, while a slurry is dragged into the pad-wafer interface to assist in planarizing the wafer surface. Due to stress concentration, the interfacial contact stress near the wafer edge generally is much higher than that near the wafer center, resulting in a spatially nonuniform material removal rate and hence an imperfect planarity of the wafer surface. Here, integrating theories of fluid film lubrication and two-dimensional contact mechanics, we calculate the interfacial contact stress and slurry pressure distributions. In particular, the possibility of using a multizone (i.e., piecewise constant) wafer-back pressure profile to improve the contact stress uniformity is examined by studying a particular case with realistic parameter settings. The numerical results indicate that using a two-zone wafer-back pressure profile with optimized zonal sizes and pressures can increase the "usable" wafer surface area (within which the average contact stress nonuniformity is below 0.1%) by as much as 12%. Using an optimized three-zone wafer-back pressure profile, however, does not increase the usable wafer surface area much further.