Fibrous calcium sulphate occurs in nature mainly as gypsum (satinspar) in extensional veins. Several mechanisms have been put forward to account for these veins and their fillings, but a number of features remain unexplained or are not in accord with the interpretation(s) given. This paper describes anhydrite as a fibrous vein precipitate, which shows most features typical of satinspar: subhorizontal attitude of the vein(s), vertical fibres, a parting separating a lower from an upper seam and incorporated wall rock fragments. New observations include the stacked nature of the fibres, pressure shadows next to wall rock fragments and parabolic alignment of the latter. These features suggest that the veins opened due to vertically-oriented tensile stress. The vein-filling crystals grew centrifugally outwards from the initial plane of rupture, which now forms the parting, keeping pace with the dilation. The mode of incorporation of wall rock fragments in the fibres requires repeated differential opening of the fissure. Thereby, either wall rock/fibre interface ruptured at a time, and statistically the ruptures alternated so that trace element trends across the vein(s) are roughly symmetrical to the parting. The source of the calcium and sulphate ions may have been adjacent evaporite beds, but an ‘external’ source is indicated where no evaporite beds are present. In contrast to previous interpretations, hydration of anhydrite to gypsum in the host rocks is not a prerequisite for the formation of satinspar veins. The exact causes for the vertical dilation remain somewhat speculative and may have been different in various locations. The vertically-oriented tensile stress may have resulted from lateral (tectonic) compression, or hydraulic overpressure, or a combination of the two.