Palaeoshorelines around four large lakes in central Tibet record a latest-Pleistocene-to-Holocene high stand during which the lakes were filled 150-200m more deeply than they are at present. GPS measurements of shoreline elevations around Zhari Namtso show that they are horizontal to within ±2m at the 2-σ level. Measurements of height made by combining Shuttle Radar Topographic Mission elevations with Google Earth imagery of shorelines around Zhari Namtso, Tangra Yumtso, Taro Tso, and Ngangla Ringtso show that all the palaeoshorelines are horizontal within measurement uncertainty. Support of the lake loads by elastic stresses can explain the horizontality of the shorelines only if the equivalent elastic thickness of the crust exceeds 15-25km. The observations are more plausibly explained by support of the lake loads through viscous stresses in the middle to lower crust. This support requires that the viscosity of the middle to lower crust is at least 1019-1020 Pa s. These values are consistent with estimates from studies of post-seismic relaxation after large earthquakes of the region and are higher, by two orders of magnitude, than would permit significant lateral flux of material through a channel in the middle to lower crust. © 2013 The Authors.