In this research, the rotary-wing blade with an on-blade Trailing-Edge-Flap (TEF) is considered in hover. The wake induced effect is included. Peters' generalized deformable blade aerodynamic theory is used for the formulation of the TEF model on the rotor blade. The Galerkin's method is employed to solve the coupled system. This study examined the effects that changing the TEF position and chord-wise size on the physical performance of this system. This research also found that changing the TEF's span-wise hinging position, the lift and torsional moment generated by the blade increases as the value of the TEF span-wise hinging position increases. Several nonlinear dynamics on the blade associated with the TEF effects were discovered in this research as well. The methodology of this paper and the results derived in this study will be of use to both the helicopters and wind turbine blades.