Abstract: This paper presents shakedown analysis of a half-space obeying Von-Mises criterion under Hertz loads in plane strain model. Based on the static shakedown theorem, a rigorous shakedown solution is established by searching for the best critical residual stress field. This method avoids the operation of mathematical programming in traditional method of shakedown analysis, and therefore obstruction since the large scale mathematical programming is overcome. It shows that both of the shakedown limit and rigorous shakedown limit increase with increasing the yield stress but decrease with the frictional coefficient. The critical residual stress fields all lie between two residual stress limits, which intersect beneath the surface for small value of μ, while tend to converge at the half-space surface when μ = 0.3, indicating that the failure mode of the material changes from subsurface failure to surface failure when increasing the frictional coefficient μ. This study has significance reference in application of shakedown analysis to the design of high-speed railway.