This paper presents a laboratory investigation of the strain-dependent dynamic properties of volcanic granular soils composed of a rhyolitic crushed rock along with additional experiments on quartz sand through a high-amplitude resonant column testing program. The sands were tested in a dry state in torsional mode of vibration and thus the degradation of the normalized shear modulus and the increase of damping ratio in shear as a function of the shear strain amplitude (γ) were examined. It was revealed that, for a given mean effective confining pressure (σ′m) and coefficient of uniformity (Cu), the volcanic sands showed higher linearity in comparison to the quartz sands and that this trend became more pronounced with decreasing σ′m and increasing Cu. In contrast to the general trend observed in the quartz soils, the confining pressure and the grain-size characteristics hardly affected the rate of normalized modulus degradation and damping increase in the volcanic sands. These differences are possibly related to the micro-mechanisms that dominate at particle contacts in the range of small to medium shear strain amplitudes. For example, the possible more pronounced crushing of the asperities during the elevation of the confining pressure and during the dynamic loading along with the lower inter-particle friction angle and stiffness of the volcanic sands of crushable particles in comparison to the quartz sands of stronger particles might play an important role in the energy dissipation during the dynamic excitation and thus on the rate of damping increase or modulus degradation.