The flow around airfoils being an energy tank; instabilities are then possible, leading often to dangerous vibratory levels. In order to predict and control aeroelastic instabilities, this investigation aims to provide a detailed understanding of the flow interaction within the complex geometry of moving blades cascade. Among the working parameters, we consider the effect of the pressure rate on the blades aeroelastic instabilities under an unsteady compressible flow. We investigate the consequences of the airfoil motion onto the aerodynamic performances, the energy transfer between the flow and the structure and the aerodynamic stability. The nonlinear aeroelastic model is based on a dynamic fluid code, a structure code and a weak coupling algorithm. Numerical simulations are conducted in three airfoil situations: fixed, pitching and free motions. The simulation results show that the pressure rate has an effect on the blade aeroelastic instabilities, their amplitude and their type: flutter and limit cycle oscillations (LCOs). The oscillation amplitude and the energy transferred to the airfoil increase more rapidly as the pressure rate increases. These instabilities have significant effects on the aerodynamic loads. Analysing the energy exchange and the aerodynamic work, we note that the aerodynamic stability is very sensible to the pressure ratio.