The paper describes the mathematical model of the rotational oscillations of the elastically fixed cylinder with flat stabilizer in the airflow. The cylinder has the single degree of freedom. It can rotate around axis that is perpendicular to cylinder axis and air velocity vector. The ratio of the length and the diameter of the cylinder is equal to 2. The model predicts the oscillation of the cylinder with constant amplitude. Two cases are considered. In the first case, the cylinder has only stabilizer. In the second case, the cylinder has not a stabilizer and is supported by elastic holder. Predictions of the mathematical model are verified in the wind tunnel experiments.