A literature review confirms that the effect of mineral composition on the strength properties of rocks has rarely been studied. One of the most problematic sedimentary rock types is sulfate rocks, which cause engineering problems in infrastructure sites such as reservoir dams. In this paper, for the first time, the effect of mineral composition on the strength properties of sulfate rocks was investigated. Rock blocks were collected from Gachsaran Formation outcrops at four reservoir dam sites under construction in Iran. After preparation, drying and saturation of the rock core samples (329 samples), uniaxial compressive strength tests were performed in accordance with ASTM and ISRM standards. The results of this study confirmed the following: (1) there is a correlation between the mineral composition and the strength properties of the sulfate rocks but the obtained relationships do not have the necessary certainty to be used as predictive equations; (2) by increasing the amount of anhydrite or microcrystalline carbonates in a gypsum rock, its strength properties are improved; (3) in a dry condition the dominant failure mode in gypsum and anhydrite rocks is a shear and dilatation mode, respectively, but after saturation, the failure mode tends to be a shear mode.