In this paper, numerical simulation of stall flutter for full annulus NASA Stage 35 is conducted using a fully coupled fluid/structure interaction. Time accurate compressible 3. D Navier-Stokes equations with Spalart-Allmaras turbulence model are solved with a system of 5 decoupled structural modal equations in a fully coupled manner. The 3rd order WENO scheme for the inviscid flux and 2nd order central difference for the viscous terms are used to accurately capture the interactions of the fluid and structure. Delayed detached eddy simulation is also applied to predict the flow induced vibration at near and stall conditions for comparison. The mechanism and aerodynamic damping behavior causing the stall flutter are analyzed. The effect of rotor stator interaction on the onset of flutter is studied. The fully coupled FSI simulation shows that Stage 35 has stall flutter at rotating stall.