Abstract: The double-sliding free-rotating model, double-shearing model and double-slip and rotation rate model (DSR² model) are three types of double-shearing kinematic models, which formulate the plastic flows of granular materials. These models incorporate different physical interpretations of angular velocity. A developed distinct element method program NS2D is used to generate assemblages which are composed of elliptical particles with aspect ratios of 1.4 and 1.7, respectively. The assemblages are then subjected to undrained simple shear tests to validate the above-mentioned models. The results show that: (1) the postulation in the double-sliding free-rotating model seems to be unduly restrictive for not considering the effect of particle rotation on energy dissipation; (2) a quantitative and qualitative difference between the observed rotation rate of the major principal stress axes and the theoretic angular velocity does not support the double-shearing model; (3) the DSR² model presents a successful prediction of the angular velocity by means of the averaged micro-pure rotation rate (APR), and it can be used to study the non-coaxiality of granular materials; and (4) the APR is a rational and important variable which considers the effect of particle rotation in the energy dissipation process, and bridges discrete and continuum granular mechanics.