In this paper, we consider the technologically important problem of periodically forced spheroids in simple shear flow and demonstrate the existence of chaotic parametric regimes. The approach used by Strand (1989) (for the Strong Brownian limit) is inappropriate in the chaotic regimes corresponding to the weak Brownian limit. Our results also indicate a strong dependence of the solutions obtained on the aspect ratio of the spheroids. This strong dependence on the aspect ratio may be utilized to separate particles from a suspension of particles having different shapes but similar sizes.