To obtain an experimental background for the description of mechanical properties of fibrous tissues of carotid atheroma, a cohort of 141 specimens harvested from 44 patients during endarterectomies, were tested. Uniaxial stress–strain curves and ultimate stress and strain at rupture were recorded. With this cohort, the impact of the direction of load, presence of calcifications, specimen location, patient’s age and sex were investigated. A significant impact of sex was revealed for the stress–strain curves and ultimate strains. The response was significantly stiffer for females than for males but, in contrast to ultimate strain, the strength was not significantly different. The differences in strength between calcified and non-calcified atheromas have reached statistical significance in the female group. At most of the analysed stress levels, the loading direction was found significant for the male cohort which was also confirmed by large differences in ultimate strains. The representative uniaxial stress–strain curves (given by median values of strains at chosen stress levels) were fitted with an isotropic hyperelastic model for different groups specified by the investigated factors while the observed differences between circumferential and longitudinal direction were captured by an anisotropic hyperelastic model. The obtained results should be valid also for the tissue of the fibrous cap, the rupture of which is to be predicted in clinics using computational modelling because it may induce arterial thrombosis and consequently a brain stroke.