CT slice data and data files from CT scans of two rock samples each containing multiple fossil specimens of Orbisiana simplex, including the holotype, alongside the publication arising from this work (Kolesnikov et al., 2018). Specimens Orbisiana_1 and Orbisiana_2 were scanned. Specimens arise from the Soligalich R-1 borehole, taken from the East European Platform of Russia (see locality map in Kolesnikov et al., 2018). For each specimen, individual folders contain the tif stack of slice images (also available as bmp files); a ctdata file listing project angle details; and xtekct files in .xml and .xtekct formats. These specimens represent important material of Orbisiana simplex, and are pyritised within a mudstone matrix. They are therefore perfect for non-destructive CT scanning to reveal their 3D morphology, as part of a collaboration with IPGG Novosibirsk. For more information, please see; https://doi.org/10.1016/j.precamres.2018.08.011