Computational modelling to calculate the mechanical loading within atherosclerotic plaques has been shown to be complementary to defining anatomical plaque features in determining plaque vulnerability. However, its application has been partially impeded by the lack of comprehensive knowledge about the mechanical properties of various tissues within the plaque. Twenty-one human carotid plaques were collected from endarterectomy. The plaque was cut into rings, and different type of atherosclerotic tissues, including media, fibrous cap (FC), lipid and intraplaque haemorrhage/thrombus (IPH/T) was dissected for uniaxial extension testing. In total, 65 media strips from 17 samples, 59 FC strips from 14 samples, 38 lipid strips from 11 samples, and 21 IPH/T strips from 11 samples were tested successfully. A modified Mooney–Rivlin strain energy density function was used to characterize the stretch–stress relationship. The stiffnesses of media and FC are comparable, as are lipid and IPH/T. However, both media and FC are stiffer than either lipid or IPH/T. The median values of incremental Young’s modulus of media, FC, lipid and IPH/T at λ = 1 are 290.1, 244.5, 104.4, 52.9, respectively; they increase to 1019.5, 817.4, 220.7 and 176.9 at λ = 1.1; and 4302.7, 3335.0, 533.4 and 268.8 at λ = 1.15 (unit, kPa; λ, stretch ratio). The material constants of each tissue type are suggested to be: media, c1 = 0.138 kPa, D1 = 3.833 kPa and D2 = 18.803; FC, c1 = 0.186 kPa, D1 = 5.769 kPa and D2 = 18.219; lipid, c1 = 0.046 kPa, D1 = 4.885 kPa and D2 = 5.426; and IPH/T, c1 = 0.212 kPa, D1 = 4.260 kPa and D2 = 5.312. It is concluded that all soft atherosclerotic tissues are non-linear, and both media and FC are stiffer than either lipid or IPH/T.