This paper describes the Raman and infrared spectroscopy of SrSO4 or celestine from the Muschelkalk of Winterswijk, The Netherlands. The infrared absorption spectrum is characterised by the SO42-modes V1 at 991 cm-1, v3 at 1201, 1138 and 1091 cm-1, and v4 at 643 and 611 cm-1. An unidentified band is observed at 1248 cm-1. In the Raman spectrum at 293 K the V1 mode is found at 1000 cm-1 and is split in two bands at 1001 and 1003 cm-1 upon cooling to 77 K.The v2 mode, not observed in the infrared spectrum, is observed as a doublet at 460 and 453 cm-1. The v3 mode is represented by four bands in the Raman spectrum at 1187, 1158, 1110 and 1093 cm-1 and the v4 mode as three bands at 656, 638 and 620 cm-1. Cooling to 77 K results in a general decrease in bandwidth and a minor shift in frequencies. A decrease in intensities is observed upon cooling to 77 K due to movement of the Sr atom towards one or more of the oxygen atoms in the sulfate group.