<p>A number of hollow-cylinder torsional shear tests were done in the drained condition to investigate the strength and deformation behaviour of rubber–sand mixtures (RSMs) at various major principal stress orientations (<i>α</i>_<i>σ</i> = 0°~90°). The test results indicate that the addition of rubber particles makes the shear strength of granular soils reduce and the volumetric contraction increase, with the minimum shear strength and maximum volumetric strain occurring around <i>α</i>_<i>σ</i> = 45°~75° for RSMs. The stress–dilatancy relationship can be described by a linear function for pure sand and a cubic function for RSMs, which is revealed to be also dependent on the major principal stress orientation <i>α</i>_<i>σ</i>. The phenomenon of stress–strain non-coaxiality is observed for both pure sand and RSMs at <i>α</i>_<i>σ</i> = 15°, 30°, 60°, and 75°, and the strength envelope takes on an asymmetric semicircular shape in the deviatoric stress plane. The occurrence of the minimum shear strength at <i>α</i>_<i>σ</i> = 45°~75° is correlated with a relatively small orientation difference between the mobilized shear plane and the bedding plane at <i>α</i>_<i>σ</i> = 45°~75°; a small orientation discrepancy between these two planes makes particles easily slide and experience a less marked interlocking effect along the shear failure plane. Furthermore, the stress–strain non-coaxiality is clarified from a theoretical perspective, through an analysis of plastic strain increment development based on the strain Mohr circle and conceptual model.</p>