A numerical simulation of one-way and two-way coupled FSI has been performed for a 2D rectangular cylinder situated in a water channel. The effect of flow velocity and aspect ratio (AR) on the rigid and flexible structures is investigated with the help of vortex-shedding frequency (f), velocity-swirling strength (λci), and total deformation (U). An accelerating-decelerating velocity field is applied to the flow field after the flow gets fully developed to observe the effect of wave impact on a rigid and flexible structure. The results have been compared for both domains to differentiate the flexible body from the rigid body. It has been found that by increasing the flow velocity, the f, λci, and U increase, whereas by increasing the AR, the U increases while the f and λci decrease. The study reveals that the Strouhal number (St) of the structure changes when we change the AR of the structure but remains constant when we change the flow velocity. The comparison of coupling shows that one-way coupling underestimates the structural deformation for low AR and high velocity but overestimates the deformation for high AR. In some cases, the solution of one-way coupling gives promising results equivalent to two-way coupling.