In this work a nature of an anisotropy of positive and negative thermal expansion of langbeinite-, arcanite- and metathenardite-type compounds is explained in terms of crystal structure data. The linear αL thermal expansion coefficient for the langbeinite and arcanite-type compounds varies from 11 to −15 and 71 to −10 ∙10−6 °С−1, respectively, while the metathenardite ones expand almost positively and negatively only along the a axis (αa = −14 ∙ 10−6 °С−1 in the range 475–600 °C). Thermal expansion of Rb2SO4 and langbeinite-type Rb2Ca2(SO4)3 is investigated by high-temperature powder X-ray diffraction in temperature ranges 25–900 and 25–1000 °C, respectively. A temperature-induced structural phase transition Pmcn↔P63/mmc (or β– ↔ α–Rb2SO4) is observed at 663 ± 12 °C. Crystal structure of the high-temperature α–Rb2SO4 was refined at 700 and 1000 °C. Thermal expansion of Rb2SO4 is highly anisotropic: αa = 35.9(1), αb = 28.9(2), αc = 70(1)∙10−6 °С−1 for β–Rb2SO4 (at 300 °C); αa = 55(5), αc = 115(9)∙10−6 °С−1 for α–Rb2SO4 (at 800 °C). The anisotropy of the expansion of both Rb2SO4 modifications is explained by a rotation of the SO4 tetrahedra. Crystal structure of the langbeinite-type Rb2Ca2(SO4)3 is described in terms of M(TO4)6 microblocks. Calculated αa thermal expansion coefficient for Rb2Ca2(SO4)3 is equal to 10.4(2) ∙ 10−6 °С−1 (at 25 °C). Main structural mechanisms of the expansion of Rb2Ca2(SO4)3 are “rocking” polyhedra and hinge deformation of the M(TO4)6 microblocks.