Waste automobile tires are used as additives or replacements instead of traditional materials in civil engineering works. In geotechnical engineering, tires are shredded to certain sizes and mixed with soil, especially used as backfill material behind retaining walls or fill material for roadway embankments. Compared to soil, rubber has high damping capacity and low shear modulus. Therefore, it requires the determination of the dynamic characteristics of rubber/soil mixtures. In this paper, the cyclic behavior of recycled tire rubber and clean sand was studied, considering the effects of the amount and particle size of the rubber and confining stresses. A total of 40 stress-controlled tests were performed on an integrated resonant column and dynamic torsional shear system. The effects of the relative size and proportion of the rubber on the dynamic characteristics of the mixtures are discussed. The dynamic properties, such as the maximum shear modulus, strain-dependent shear modulus, and damping ratio, are examined. For practical purposes, simple empirical relationships were formulated to estimate the maximum shear modulus and the damping ratio. The change in the shear modulus and damping ratio with respect to shear strain with 5% of rubber within the mixture was found to be close to the behavior of clean sand.