For seismic stations deployed on ice sheets, determining crustal structure using P wave receiver functions can be difficult since ice reverberations may mask P-to-S (Ps) conversions from the crust-mantle boundary (Moho). In this study, we assess the usefulness of S wave receiver functions (SRFs), which are not affected by ice multiples, for investigating crustal structure beneath ice sheets by analyzing broadband seismic data recorded across the Transantarctic Mountains (TAMs) and the East Antarctic (EA) craton. Clear S-to-P (Sp) conversions from the Moho are obtained using standard SRF processing methods and are easier to interpret than the corresponding Ps conversion on PRFs. When the Sp-S times are modeled together with 16-20 s Rayleigh wave group velocities, we obtain Moho depth estimates of similar to 40-45 km for the EA craton, consistent with average Precambrian crustal thickness found globally but similar to 9 km thicker than previously reported estimates. A somewhat thinner crust (similar to 35-40 km) is obtained beneath the TAMs, suggesting that crustal buoyancy is at most a minor contributor to the uplift of the mountain range in this region.