Four different microstructure constitutive equations (CEs) for discotic nematic liquid crystals based on Doi＇s modified nematodynamics theory are formulated. Their dynamic and steady state responses under simple shear flows are computed and analyzed in terms of the tensor order parameter Q, the orientation director triad (n, m, 1), and the uniaxial S and biaxial P alignments. A unit sphere description of the director triad is used to characterize and classify the various predicted stable orientation states, and to discuss and analyze their multistabilities as a function of dimensionles shear rate. Various attractors, steady and periodic, are also identified and their stability is discussed in detail for all the CEs. A validation procedure based on the predicted microstructural response along with bifurcation diagrams of the individual CE and representative experimental observations as well as theoretical results is implemented, and used to select the most appropriate CE. The selected CE predicts, under shear; the simultaneous presence of stable in-plane (steady and periodic) states and out-of-plane steady state, and the classical transition among the in-plane periodic and steady states with increasing shear rate. The excellent performance of the selected CE in shear flows strongly suggests that it is a reliable contribution towards the formulation of a process model for mesophase pitch spinning.