Surface waves from earthquakes recorded during the two-year Southern Africa Seismic Experiment have been used to estimate the average velocity structure beneath the Kaapvaal craton. By cross-correlating the data with synthetics derived using mode summation techniques, I measure frequency-dependent phase delays for Love and Rayleigh waves, as well as higher modes, for 12 events ranging in epicentral distance between 12¿ and 91¿. I simultaneously invert the traveltime delays for structure beneath the array and outside of the array. In this way, heterogeneity along the path lying outside of the array is not mapped erroneously into structure beneath the array. The differential dispersion between the Love and Rayleigh waves require some anisotropy in the upper mantle; however, models with a range of anisotropic depths (as shallow as 150 km and as deep as 220 km) can equally well fit the data. The sensitivity of the fundamental mode surface waves used in this study begins to decline significantly below ~200 km depth limiting interpretation of deeper structure. Nonetheless, this range of anisotropic depths is significantly different than the 100 km depth proposed in a recent study by Freybourger et al. <2001> using a similar technique and different data from the same array. I attribute the difference in their dispersion measurements and modeling to the improper use of a phaseless (i.e. frequency-dependent) filter on the data, which systematically biased their measurements at lower frequencies. In addition, I find no evidence of a low-velocity layer as proposed by Qui et al. <1996> and Priestley <1996>.