In this paper, anhydrous calcium sulphate CaSO4 (anhydrite) is considered as a carrier material for organic matter delivery from Space to Earth. Its capability of incorporating important fractions of water, leading to different species like bassanite and gypsum, as well as organic molecules; its discovery on Mars surface and in meteorites; the capability to dissipate much energy by its chemical decomposition into solid (CaO) and gaseous (SO3) oxide, make anhydrite a very promising material in an astrobiological perspective. Since chemical cooling has been recently considered by some of the present authors for the case of Ca/Mg carbonates, CaSO4 can be placed into a class of ‘white soft minerals’ (WSM) of astrobiological interest. In this context, CaSO4 is evaluated here by using the atmospheric entry model previously developed for carbonates. The model includes grain dynamics, thermochemistry, stoichiometry, radiation and evaporation heat losses. Results are discussed in comparison with MgCO3 and CaCO3 and show that sub-mm anhydrite grains are potentially effective organic matter carriers. A Monte Carlo simulation is used to provide distributions of the sulphate fraction as a function of altitude. Two-zone model results are presented to support the isothermal grain hypothesis.