The usage of scrap tires as construction materials in civil engineering is one of the most promising ways in recycling this troublesome waste material. In order to investigate the effect of adding granulated rubber in improving the performance of sand, the compressibility and shear properties of granulated rubber-Fujian sand mixtures was studied by confined compression tests and direct shear tests. The influence of rubber content and water content on the mechanical characteristics of rubber-sand mixtures were studied, and a hyperbolic model was established to predict the shear stress-strain relationship of rubber sand. The research findings are as follows:The compression deformation of rubber-sand mixtures increases with the rubber content, and the compression deformation of saturated mixtures is greater than that of the dry mixtures. The shear stress-horizontal displacement curve of rubber-sand mixtures shows a strain-hardening characteristic. There is no obvious relationship between shear strength and rubber content, and the pore water has great influence on internal friction angle of rubber sand. The internal friction angles of dry samples decrease with the increase of rubber content. The internal friction angles of saturated samples increase with the rubber content. The hyperbolic constitutive model can be used to predict the shear stress-displacement relationship of rubber sand.