The natural passive flight of a falling leaf is a captivating fluid-solid interaction problem. To resolve their perplexing trajectories, falling leaves have been traditionally modeled as rigid plates. However, the falling of such flat bodies are accompanied by some deformation, which plays an important role in their flight dynamics. This study simulates the flight patterns of freely falling flexible plates in a two-dimensional viscous fluid using direct numerical simulations. Plates of different bending rigidity are analyzed. Results show that flexibility alters the flight state of a falling plate. The changes in flight states with respect to bending stiffness are mapped. This is in addition to the flight states established within ranges of moment of inertia and Reynolds numbers. The coupling effect between the plate deformation and its generated wake is analyzed via flow field and surface pressure relationships. The analysis reveals that the predominate effects are the recirculation of wakes and surface pressure distribution. From those effects, the plates have generated unique flight patterns that have not been previously observed for rigid plates, such as periodic "chaotic" flights and interesting twirling motions.