With the increase of vehicle running mileage, the stability of the vehicle decreases due to the deterioration of wheel-rail matching relationship. The vehicle running performance can be improved by modifying the wheel profile with different flange thickness. However, the dynamic performance of the wheel profile with different rim thickness and rail matching is unknown. According to the matching of tread surface and CHN60 with four kinds of different flange thickness in LMB series, the paper makes simulation calculation with the change of wheel-rail contact point position and contact area distribution. By calculating contact width and contact concentration, the change rule of contact geometry caused by wheelset profile is analyzed. Combined with wheel-rail contact point movement and wheel-rail contact bandwidth variation, the nonlinear contact geometric relationship parameter λTC is defined. The parameter λTC describes the stability of EMU in service in the case of two or more wheel-rail matches. The results show that as the thickness of wheelset rim increases, the contact width of wheelrail contact point on the wheel tread increases, but the contact concentration decreases.With the increase of the geometric λTC parameters of the nonlinear wheel-rail contact, the vehicle dynamics parameters decrease, and thenonlinear equivalent taper and λNP show a descending and stationary state respectively.The nonlinear wheel-rail contact geometric λTC parameters can well show the strength of the stability of EMU in service when the wheelset with different rim thickness is matched with the rail, and can accurately reflect the variation of vehicle vibration response.