Brownian dynamics simulations have been carried out for suspensions of oblate spheroidal particles interacting via the Gay‐Berne potential. The system changed from isotropic phase to nematic one with increasing the particle concentration. In addition, the behavior of particles in simple shear flows was simulated; the shear was imposed on the systems in nematic phase at rest. The systems exhibited various motions of the director depending on the shear rate, e.g. continuous rotations of director at low shear rates and flow aligning at high shear rates.