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.