In this paper, an approach of the formulation for Hertzian contact problem between wheel and rail is presented. This formulation used analytic and numerical approach, especially in solving elliptic integrals in order to obtain dimension relations of the contact, deformation, contact pressure and stress contours. The main curvature radius range of the smaller rail are from 300-260 mm. Modeling with finite element solution was also performed as an alternative approach solution to the contact pressure. Besides, it is with Finite Element Method (FEM) can show the contact stress distribution and the influence of contact at a certain depth. The result of this formulation and Finite Element approach are compared with the model equation by Fischer and Wiest [1] and the exact value calculated by Hertz's equation [2]. The results showed that the calculation of the contact dimensions and maximum contact pressure give more conform results. The difference results obtained by the method of Hertz are between 1.47-2.37% for the maximum contact pressure and 2.45-3.02% for the major axis the ellipse. The difference results using finite element method also gives conforming results of 0.09-3.5% for the maximum contact pressure
