Several studies show that scrap tyre rubber mixed with sand is an effective and sustainable method for mitigating vibrations. The dynamic and cyclic response of this composite soil has already been investigated. However, layered sand-rubber configurations have not been considered yet. This study reports findings of resonant column tests on three types of specimen: (a) sand-only or rubber-only, (b) layered sand-rubber, and (c) sand-rubber mixtures. The analysis allowed for an evaluation of the maximum shear modulus and its degradation with strain over a wide range of confining stress and shear strain. The evolution of the damping ratio with strain was determined analogously. Effects of pre-loading and pre-straining were also considered. The results show that the behaviour of layered specimens is much more similar to that of pure rubber than to sand-rubber mixtures, with very low shear modulus values, smaller degradation of stiffness with strain and pre-loading, and higher damping. For example, at the confining stress of 100 kPa and rubber content of 0/33.3/50/67.7/100% by volume, the small strain shear moduli for sand-rubber mixtures are equal to 98.3/30.4/15.4/7.1/1.3 MPa and 98.3/3.6-4.2/2.4-2.8/2.1/1.3 MPa for sand-rubber layered specimens, depending on the arrangement of layers. A shear beam model is shown to be adequate for calculating the response of the layered specimens comprising layers of large stiffness contrast.