Incorporating recycled rubber particles from end-of-life tires into concrete is widely acknowledged as an effective method for addressing the significant environmental challenges posed by the increasing accumulation of waste tire rubber. This study proposes a series of experimental and analytical studies on the mechanical behaviour of concrete materials incorporating recycled tyre rubber particles, namely rubberised concrete (RuC), under triaxial loading situations. The failure modes, accompanied by scanning electron microscope photography, were used to analyse the fracture mechanisms both at macro- and microscopic scale. RuC mixes with various volumetric rubber replacement ratios of both fine and coarse aggregates were prepared. Multiple levels of lateral confinements on cylindrical specimens were chosen to investigate the effect of confinement ratio on the compressive performance of RuC. The maximum bearing capacity of conventional concrete increases by 532 % as the confinement ratio increases from 0 % to 100 %, whereas its counterpart for RuC with 40 % rubber content is 227 %. The crushing strain of RuC increases with the lateral confinement ratio, and it is observed that the rubber content has a positive influence on the increase ratio. A systematic analytical model was firstly proposed for the detailed assessment of the complete triaxial stress-strain response of RuC. The experimental and analytical findings allowed for the investigation of the failure criteria of RuC under compression, and the model denoting the compressive meridian is proposed. Validations against the test results from this study indicate that the proposed expressions offer reliable predictions of the mechanical properties and constitutive response under the investigated loading conditions. These findings provide essential insights for sustainable infrastructure development, enabling effective utilisation of waste tyre rubber in critical structural applications.