The behaviour of granular material was investigated by simulating an undrained triaxial compression test for three-dimensional assembly of ellipsoid particles over a wide range of void ratio, e, and mean confining stress, p′. The assembly was either isotropically consolidated or K0 consolidated prior to undrained shearing up to 30%axial strain to reach steady-state conditions. Aunique steady-state linewas obtained, irrespective of the consolidation path. The micro-mechanical quantities, such as coordination number and von Mises fabric in terms of second invariant of deviatoric fabric, FvM, also reached steadystate values. The normalised anisotropic fabric variable, A, and the trace of the joint stress–fabric tensor, KF, evolved during undrained simulation and reached the steady-state value at the end of shearing. This forms a unique relationship in KF–p′–e space and the projection of this relationship in e–log(p′) space is the classical steady-state line. This underpins the concept of fabric evolution and steady-state fabric in anisotropic critical state theory. The relationships of state parameter, ψ, and stress ratio at instability, ηIS=(q/p′)IS, were dependent on consolidation path, and the difference was not related to coordination number, but to FvM. However, a new phenomenon was observed that stress ratio, η, at the end of K0 consolidation and ηIS may reach beyond the steady-state stress ratio, M. Experimental data are needed to verify this; until then such behaviour should be regarded as unproven.