The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades. The formulation is based on the finite volume method. By applying the TVD scheme to the linear unsteady calculations, the precise calculation of the peak of unsteady aerodynamic forces at the shock wave location like the delta function singularity becomes possible without empirical constants. As a further feature of the present paper, results of the present numerical calculation are compared with those of the double linearization theory (DLT), which assumes small unsteady and steady disturbances but the unsteady disturbances are much smaller than the steady disturbances. Since DLT requires far less computational resources than the present numerical calculation, the validation of DLT is quite important from the engineering point of view. Under the conditions of small steady disturbances, a good agreement between these two results is observed, so that the two codes are cross-v The paper presents the formulation to compute numerically the unsteady aerodynamic forces on the vibrating annular cascade blades. The formulation is based on the finite volume method. at the shock wave location like the delta function singularity becomes possible without empirical constants. As a further feature of the present paper, results of the present numerical calculation are compared with those of the double linearization theory (DLT), which assumes small unsteady and steady disturbances but the unsteady disturbances are much smaller than the steady disturbances. Since DLT requires far less computational resources than the present numerical calculation, the validation of DLT is quite important from the engineering point of view. Under the conditions of small steady disturbances, a good agreement between these two results is observed, so that the two codes are cross-v