The stockpiling of waste tires at landfill sites has become a nuisance for the society. One of the alternatives could be converting the recycled rubber into powdered form and mixing it with soil to use it as the backfill of the retaining structures. This paper is based on the study of such sand-rubber mixtures. In this work, Discrete Element (DEM) simulations were employed to study the mechanical response of sand-rubber mixtures with respect to a column of grains enclosed within a rigid cylindrical confinement, and subjected to an oedometric compression by the fixed velocity displacement of one of the horizontal walls. Further, experimental analysis was also carried out by using a uniaxial load cell to load the sand-rubber mixtures under compression. Different initial packings of sand-rubber mixture were prepared by varying: (a) the packing volume fraction and (b) the volume fraction of rubber. The mechanical response at small strains was studied for these sand-rubber packings. The mixture behavior was observed to be more sand-dominant or rubber-dominant depending on the rubber fraction and the mixture quality. Moreover, variation in the initial volume fraction of the packing also caused a difference in the load bearing of the packings for a given strain and a given rubber fraction.