In order to study the shimmy problem of the 4-wheel independent driving electric vehicles with the non-independent front suspensions, a 3-DOF dynamics model is established using the Lagrange Equation. The tire nonlinearity is considered in the model with a Magic Formula tire model. Both theoretical methods and numerical simulations are adopted to analyze the stability of the system and verify each other. The results of system phase portrait diagrams show that bifurcation occurs at a specific longitudinal speed, which is identified as the system dynamic critical speed.