Flutter, a very important phenomenon in the field of aeroelastic analysis of wings and fins, is characterized by zero net damping and self-sustained oscillations. The type of turbulence modeling approach is critical to the accurate prediction of flutter. In the current paper, the effects of different turbulence models on the aeroelastic flutter characteristics of AGARD 445.6 wing in transonic flow are investigated using a strongly coupled twoway fluid structure interaction (FSI) methodology. A finite volume method-based Navier-Stokes fluid flow solver is strongly coupled with a finite element method-based structural dynamics solver using a coupling module, all in the commercial CFD software ANSYS. Three different turbulence models based on the Boussinesq eddy viscosity hypothesis namely SST k-ω model, Realizable k-ε model and modified Spalart - Allmaras model with curvature correction modifications are considered. Time integration of the governing structural dynamics equation is performed using HHT-α method with Newton - Raphson linearization. Wing tip deformation and energy characteristics are evaluated at different dynamic pressures by varying the free stream velocity to observe zero damping and diverging response. Furthermore, the flow field around the wing is investigated and eddy viscosity, turbulent kinetic energy and turbulence dissipation rate contour plots at various spanwise locations are presented as well. Results show that in the transonic regime studied here, the SST k-ω model predictions are worse than the modified Spalart-Allmaras model and Realizable k-ε model, in terms of the flutter onset point, when compared with experimental data.