A simulation algorithm was developed to predict the rheological properties of oblate spheroidal suspensions. The motion of each particle is described by Jeffery's solution, which is then modified by the interactions between the particles. The interactions are considered to be short range and are described by results from lubrication theory and by approximating locally the spheroid surface by an equivalent spherical surface. The simulation is first tested on a sphere suspension, results are compared with known experimental and numerical data, and good agreement is found. Results are then presented for suspensions of oblate spheroids of two mean aspect ratios of 0.3 and 0.2. Results for the relative viscosity eta (r), normal stress differences N (1) and N (2) are reported and compared with the few available results on oblate particle suspensions in a hydrodynamic regime. Evolution of the orientation of the particles is also observed, and a clear alignment with the flow is found to occur after a transient period. A change of sign of N (1) from negative to positive as the particle concentration is increased is observed. This phenomenon is more significant as the particle aspect ratio increases. It is believed to arise from a change in the suspension microstructure as the particle alignment increases.