Radial turbine featuring a Multi-channel Casing (MC) is a new design under investigation for enhancing the turbine controllability. The idea behind this new design is to replace the traditional spiral casing with a MC, which allows controlling the mass flow by means of opening and closing control valves in each channel. The arrangement of the closed and opened channel is called the admission configuration, while the ratio between the counts of the open channels to the total number of channels is called the admission percentage. Among several aspects, when applying different admission configurations, the aerodynamic damping during resonant excitation is considered during the design of the turbine. The present study aims at investigating the effect of different MC admission configurations on the aerodynamic damping as an extension to an aerodynamic forcing study, which already assessed the different forcing patterns associated with these different admission configurations. Due to the asymmetry of the flow in circumferential direction resulting from the different partial admission configurations, the computational model is solved as full 3D time-marching, unsteady flow using ANSYS CFX in a one-way fluid-structure analysis. Two different modeling approaches have been considered in this study to investigate their capability of predicting the damping ratio for different MC admission configurations: a) the conventional isolated rotor approach and b) a full model consisting of the rotor and its casing. The results show that the casing affects the aerodynamic damping behavior, which can only be captured by the full model. Furthermore, the damping ratios for all different admission configurations have been calculated using the full stage model.