Subsidence analysis of the eastern Black Sea basin suggests that the stratigraphy of this deep, extensional basin can be explained by a predominantly pure-shear stretching history. A strain-rate inversion method that assumes pure-shear extension obtains good fits between observed and predicted stratigraphy. A relatively pure-shear strain distribution is also obtained when a strain-rate inversion algorithm is applied that allows extension to vary with depth without assuming its existence or form. The timing of opening of the eastern Black Sea, which occupied a back-arc position during the closure of the Tethys Ocean, has also been a subject of intense debate; competing theories called for basin opening during the Jurassic, Cretaceous or Paleocene/Eocene. Our work suggests that extension likely continued into the early Cenozoic, in agreement with stratigraphic relationships onshore and with estimates for the timing of arc magmatism. Further basin deepening also appears to have occurred in the last ∼ 20 myr. This anomalous subsidence event is focused in the northern part of the basin and reaches its peak at ∼ 15-10 Ma. We suggest that this comparatively localized shortening is associated with the northward movement of the Arabian plate. We also explore the effects of paleowater depth and elastic thickness on the results. These parameters are controversial, particularly for deep-water basins and margins, but their estimation is a necessary step in any analysis of the tectonic subsidence record stored in stratigraphy.