The article presents an analysis of the vibrations of tubular rigid busbar located at a power station. The analysed case concerns a real-life situation involving wind acting on a circular cross-section of the busbar—considered aerodynamically stable—and on an asymmetrically iced cross-section. To determine whether the cross-section is aerodynamically unstable, Den Hartog’s criterion was examined. The critical wind velocity was established, and the area of aerodynamic instability was pinpointed. The analysis considered actual wind load values obtained from wind measurements. Based on dew point analysis and measured temperature, the extent of icing was determined. The analysis was carried out for two support configurations using dynamical formulation with Euler’s approach. To reduce the displacement amplitude, the use of a tuned mass damper was proposed.