Mechanical response of mixtures composed of glass and rubber particles are investigated in direct shear experiments in laboratory and by means of discrete element method simulations. The mixtures are prepared with different contents of rubber fractions. It is found that, with increasing rubber particles, volume phase transition occurs from dilatancy to reduction, and the elastic properties of the mixtures are improved. Experimental results show that, as the rubber particles (up to 30% in volume) are added, the value of the shear stress falls, and the volume phase transition occurs, but the critical states are the same. The shear stress is independent of shear rates, however, it grows with the normal force. We have obtained the consistent results in the simulation. Furthermore, statistical analysis of the simulation results shows that the average coordination number is raised with the increase of rubber particles. Volume phase transition occurs at low rubber fraction when the normal force is large. It is very important to keep in mind that the average coordination number is always between 5.6 and 5.9 at the phase transition points even under different normal forces. When the rubber fraction is less than 30%, the residual shear strength is nearly the same as in the system of glass beads. However, the residual shear strength decreases when the rubber particles increase to the fraction larger than 30%. Meanwhile, the residual shear strength increases with the normal pressure.