The aerodynamics of freely falling objects is one of the most interesting flow mechanics problems. In a recent study, Andersen, Pesavento, and Wang [J. Fluid Mech., vol. 541, pp. 65-90 (2005)] presented the quantitative comparison between the experimental measurement and numerical computation. The rich dynamical behavior, such as fluttering and tumbling motion, was analyzed. However, obvious discrepancies between the experimental measurement and numerical simulations still exist. In the current study, a similar numerical computation will be conducted using a newly developed unified coordinate gas-kinetic method [J. Comput. Phys, vol. 222, pp. 155-175 (2007)]. In order to clarify some early conclusions, both elliptic and rectangular falling plates will be studied. Under the experimental condition, the numerical solution shows that the averaged translational velocity for both rectangular and elliptical plates are almost identical during the tumbling motion. However, the plate rotation depends strongly on the shape of the plates. In this study, the details of fluid forces and torques on the plates and plates movement trajectories will be presented and compared with the experimental measurements.