[en] In this work the authors present the probably first realistic shell model calculation of the low-lying spectra for the unstable even Sn isotopes with mass number A=102, 104, and 106. The effective shell model interaction was derived from a realistic free nucleon-nucleon interaction employing perturbative many-body techniques. For the free nucleon-nucleon interaction a recent version of the Bonn meson-exchange potential model was used. For several of the isotopes studied experimental data are rather scare or non-existent. The spectra derived may therefore serve as a guide for identifying levels in the unstable Sn isotopes near the doubly magic ¹⁰⁰Sn core. The results were tested by calculating E2-transitions for the above nuclei. 19 refs., 2 tabs