The mixture of scrap rubber particles and sands has been extensively used as geotechnical engineering recycled materials due to its environmental protection performance, light quality and excellent energy dissipation capability. The mechanical properties of the system can be modulated by the mixing ratio between soft and hard components. But the reasons for such a change on a particle scale are not yet clear. In this paper the elastic behaviors of glass-rubber mixed particles are studied by the sound velocity measurement and discrete element simulation. The velocity of compressional wave and the dynamic effective elastic modulus of mixed sample under hydrostatic stress are measured by time-of-flight method. It is found that the wave velocity is almost constant and the modulus decreases slightly with the proportion of rubber particles increasing to 20%. After that the wave velocity and modulus decrease rapidly and the system transforms from rigid-like behavior to soft-like behavior until the proportion of rubber particles reaches to 80%. When the proportion of rubber particles are more than 80%, the compressional wave velocity and the dynamic effective elastic modulus remain stable again. Such experimental results are consistent with discrete element method analyses which provide more in-depth insights into the micromechanics of the mixture. The simulation reveals that at low rubber fraction the main force chain structure is basically composed of glass particles without rubber particles, which accounts for the phenomenon that the velocity of the compressional wave is basically constant. When the glass particles and rubber particles co-construct the main force chain structure, the distribution of the normal contact force is relatively uniform at high rubber fraction. This can be regarded as the glass particles suspending in the rubber particles. An improved effective medium theory is proposed to describe the elastic behavior of the mixed particles system. It is considered that the deformation of the internal particles is relatively uniform for glass dominated mixture which satisfies the isostress hypothesis. A parallel spring model can be used to describe the nonlinear contact model of particles in such materials. On the other hand, rubber dominated mixture approximately satisfies the isostrain hypothesis, which can be described by a series spring model. The outcomes of such models are in agreement with the simulation results for rigid glass dominated mixture and soft rubber dominated mixture. This study is helpful in exploring the mechanisms that are responsible for the macroscale elastic behavior of mixed granular material from the microscopic point of view.