A numerical approach for calculating self-excited unstable aerodynamic/aeroelastic behaviours in lurbo-machinery blading systems is described. The flow field through a cascade section with multiple blade passages (whole annulus) is governed by the 2-D unsteady Navier-Stokes equations, which are spatially discretized by using a finite volume scheme. The motion of each blade section is governed by simple rigid body spring-mass structural dynamic equations with two degrees of freedom (“bending” and “torsion”). The coupled aeroelastic equations are simultaneously integrated in time by using the 4-stage Runge-Kutta scheme. Examples of calculated results for blade rows with rotating stall and stall Mutter are presented.