Numerical simulation of non-linear vibration systems requires efficient programs and high performance computers as a means to improve computational efficiency. Based on the similarity between the mechanical system dynamics model and the simulated integral circuit, an equivalent circuit model of a 2-degree-of-freedom elastic single wheel pair with transverse non-linear vibration considering the wheel-rail gap is established, and the circuit model is simulated and analysed using Multisim. The results of the study show that the equivalent circuit simulation is consistent with the numerical simulation analysis results, except that the equivalent circuit simulation is fast and efficient overall, and the parameters can be modified in real time during the simulation run to dynamically observe the simulation analysis process. Equivalent circuit simulation provides a viable and efficient reference method for the study of non-linear system dynamics.