This article illustrates the use of near-source S-wave polarization analyses for constraining some rupture parameters of large earthquakes, in the particular case of the 1979 Imperial Valley mainshock. The ten SMA1 strong-motion records closest to the source have been studied in the 1 to 3-Hz frequency range. The records were first corrected following the analysis of Zollo and Bernard (1989), from some anisotropy that produced strong S splitting at a few sites. The rotation of the S polarization with time at most of the sites was then interpreted in terms of the northwestward propagation of the rupture. We assumed a constant focal mechanism on the fault plane (vertical strike slip). The polarization data and the absolute times at some stations allowed the identification of a set of subsources. Their location in space and time (assuming a depth of 8 km) provided a mean rupture velocity of 3.1 km/sec (±0.25 km/sec), i.e., 90% of the shear velocity. The high-frequency radiation (3 Hz) during most of the rupture thus is very likely to have been generated about 1 sec before the beginning of the low-frequency radiation (0.5 to 1 Hz) studied by Archuleta (1984). The final rupture model fits the S-polarization history well at most sites; it also constrains the anisotropy characteristics of the sediments under some sites, in particular EM0, where it is consistent with the alignment of vertical cracks in the NS stress field. Applying such a method to other earthquakes requires a careful selection of the distance and frequency range. In particular, the effect of perhaps pervasive ubiquitous anisotropy in the upper crust must be taken into account, which may require the analysis of aftershock records at the same sites.