The fluid–structure interaction is one of the most important coupled problems in mechanics. The topic is crucial for many high-technology areas. This work considers the interaction between an elastic obstacle and rarefied gas flow, seeking specific problems that arise during this interaction. The Direct Simulation Monte Carlo method was used to model the rarefied gas flow and the linear Euler–Bernoulli beam theory was used to describe the motion of the elastic obstacle. It turned out that the vibrations caused by the gas flow could provoke a resonance-like phenomenon when the frequency of vortex shedding of the flow was close to the natural frequency of the beam. This phenomenon could be useful in certain high-technology applications