Mixtures of rigid sand particles and soft fine-grained rubber particles are tested to investigate their small and large-strain responses. Mixtures are prepared with different volumetric sand fraction sf to identify the transition from a rigid to a soft granular skeleton using wave propagation, k0 loading, and triaxial testing. Deformation moduli at small, middle, and large strains do not change linearly with the volume fraction of rigid particles; instead, deformation moduli increase dramatically when the sand fraction exceeds a threshold value between sf=0.6–0.8 that marks the formation of a percolating network of stiff particles. The friction angle increases with the volume fraction of rigid particles. Conversely, the axial strain at peak strength increases with the content of soft particles, and no apparent peak strength is observed in specimens with low sand fraction (sf≤0.6). The presence of soft particles alters the formation of force chains. Although soft particles are not part of high-load carrying chains, they play the important role of preventing the buckling of stiff particle chains.