In the present investigation, a detailed numerical investigation of the flow and heat transfer characteristics of a channel with an elastic fin (vortex generator) and an elastic wall has been carried out using finite element method. The Fluid-Structure Interaction (FSI) model is used to capture the interaction between the fluid and the solid structure. A sinusoidal time dependent velocity profile has been imposed at the inlet of the channel and the right half of the upper wall of the channel is heated and exposed to constant temperature boundary condition. Due to the sinusoidal velocity profile at the inlet, the elastic fin oscillates periodically and act as a vortex generator, which causes more turbulence in the flow. The obtained results showed that the Nusselt number over the heated wall is affected by the position of the flexible fin, height of flexible fin and elasticity modulus of elastic fin. Moreover, due to the elasticity of the elastic wall and sinusoidal behavior of the inlet velocity, the elastic wall oscillates periodically upward and downward. The Nusselt number values over the heated wall are increased with decrease of the elastic modulus value of the elastic wall. However, the decrease in elastic modulus value of the elastic wall contributes to an increase in the pressure drop inside the channel. It should be added that the interplay between the fluid motion and the deformable structures leads to enhanced turbulence, as the flexible fin and elastic wall introduce additional disturbances and fluctuations into the flow regime. Consequently, this heightened turbulence level has profound implications for heat transfer processes within the system.