As existing tire models were no longer appropriate for vibration analysis of mechanical elastic wheel (MEW), elastic rope model was presented based on MEW’s structural characteristics and its hinges’ feature that transmitted force by single-direction. The single and total stiffness expression and frequency response function of the model were deduced and a complete mathematical model of MEW for vibration analysis was established. According to the model vibration, calculation under C-level random rough road input was conducted, and the center displacement response of wheel hub in time domain and power spectral density response in frequency domain were obtained. By comparing the finite element simulation results, the correctness of the elastic rope model is verified and it indicates the resonant frequencies are 19 Hz～21 Hz that provides a reference for the optimization of the MEW design.