We present strontium isotopic (⁸⁸Sr/⁸⁶Sr and ⁸⁷Sr/⁸⁶Sr) results obtained by ⁸⁷Sr–⁸⁴Sr double spike thermal ionization mass-spectrometry (DS-TIMS) for several standards as well as natural water samples and mineral samples of abiogenic and biogenic origin. The detailed data reduction algorithm and a user-friendly Sr-specific stand-alone computer program used for the spike calibration and the data reduction are also presented. Accuracy and precision of our δ⁸⁸Sr measurements, calculated as permil (‰) deviations from the NIST SRM-987 standard, were evaluated by analyzing the NASS-6 seawater standard, which yielded δ⁸⁸Sr = 0.378 ± 0.009‰. The first DS-TIMS data for the NIST SRM-607 potassium feldspar standard and for several US Geological Survey carbonate, phosphate, and silicate standards (EN-1, MAPS-4, MAPS-5, G-3, BCR-2, and BHVO-2) are also reported. Data obtained during this work for Sr-bearing solids and natural waters show a range of δ⁸⁸Sr values of about 2.4‰, the widest observed so far in terrestrial materials. This range is easily resolvable analytically because the demonstrated external error (±SD, standard deviation) for measured δ⁸⁸Sr values is typically ≤0.02‰. It is shown that the “true” ⁸⁷Sr/⁸⁶Sr value obtained by the DS-TIMS or any other external normalization method combines radiogenic and mass-dependent mass-fractionation effects, which cannot be separated. Therefore, the “true” ⁸⁷Sr/⁸⁶Sr and the δ⁸⁷Sr parameter derived from it are not useful isotope tracers. Data presented in this paper for a wide range of naturally occurring sample types demonstrate the potential of the δ⁸⁸Sr isotope tracer in combination with the traditional radiogenic ⁸⁷Sr/⁸⁶Sr tracer for studying a variety of biological, hydrological, and geological processes.