Considering the complex characteristics of the track structure in railway turnouts, it is difficult and also expensive to experimentally study rail damages; therefore, numerical methods are an effective alternative. This study presents a numerical method to simulate rail surface-initiated rolling contact fatigue in the switch panel of railway turnouts. This method includes simulation of the vehicle–turnout wheel–rail dynamic interaction, analysis of the wheel–rail multipoint non-Hertzian rolling contact that considers the relative motion between the switch and stock rails, and calculation of the accumulated rail surface-initiated rolling contact fatigue. The accumulated rail surface-initiated rolling contact fatigue after the vehicles passed a turnout switch panel 80 times (the average number of vehicles running on the Chinese high-speed railway lines per day) in the through route with facing move was simulated based on this procedure. The result showed that the maximum surface-initiated rolling contact fatigue damage of the switch rail and the stock rail was 1.57 × 10−2 and 0.62 × 10−2, respectively. Surface-initiated rolling contact fatigue in the switch rail mainly occurred at the gauge angle, and in the stock rail it mainly occurred at the center of the rail. In addition, the influence of track parameters (rail inclination, track gauge, and friction coefficient) is analyzed. The friction coefficient influenced the rail surface-initiated rolling contact fatigue. When the coefficient exceeded 0.3 in particular, the rail rolling contact fatigue damage increased sharply. Hence, suitable friction control measures should be taken during rail maintenance in order to mitigate the rail surface-initiated rolling contact fatigue damage, e.g. by keeping the wheel–rail friction coefficient below 0.3.