Atherosclerosis is characterised by the progressive growth of a plaque, where a fibrous cap covers a lipid-rich core. Rupture of this fibrous cap can lead to thrombosis and a heart attack or stroke. This dissertation considered the role of plaque microstructure in the mechanics and rupture risk of atherosclerotic plaques. Fibre structures in human atherosclerotic plaques were characterised through scanning electron microscopy, histology, and image processing. Local primary fibre orientation and the fibre dispersion were calculated. Plaque shoulder regions, where rupture is most frequent, had higher fibre dispersion and were more misaligned with the lumen wall. Comparative FE models were made from the plaque geometries and fibre structures found by image processing: one with evenly dispersed fibres (isotropic) and one with a preferred fibre orientation (anisotropic). The isotropic and anisotropic FE models predicted significantly different stresses. Stresses were often highest in the shoulder regions. Anisotropic stresses were calculated relative to fibres: axial stresses were highest, shear stresses were intermediate, and transverse stresses were low. Since the tissue is strongest in the fibre direction (axially), axial and shear failure modes should be considered. Material tests (uniaxial tension, trouser tear, and notched specimen) were used to characterise material properties in healthy porcine arteries. Fibre structures were evaluated by histology, multiphoton microscopy, and image processing. Samples were stiffer circumferentially and toughest against radial tears. Fractures progressed between fibres, rather than by breaking them. Material properties and fracture mechanisms were explained by fibre structures. In summary, atherosclerosis altered the fibre structure of the arteries, in ways that were mechanically significant and that explained clinical observations.