A numerical analysis is developed for the scattering of incident acoustic and vortical waves by an annular cascade. The mathematical formulation uses the linearized Euler equations about an axial and swirling mean flow. For nearly sonic waves, exact non-reflecting in flow/outflow boundary conditions are applied using the normal mode analysis. The system of equations are solved using an explicit compact high-order McCormack-type scheme. The method is validated by comparison with the uniform flow and narrow annulus limits.