This paper presents a two-dimensional model for the analysis of interaction between surface and internal cracks in the railheads subjected to wheel loading. The shape of the railhead, the surface crack and the internal crack are modelled as curved cracks defined by the theory of continuous distribution of dislocation in an infinite body. From the boundary conditions along these cracks, a system of singular integral equations is deduced. Influence functions in these singular integral equations are first expanded into the Cauchy kernel multiplying normal functions and later are reduced to a system of linear equations and solved numerically. Stress intensity factors (SIFs) of the surface crack tip are calculated from the numerical solution of distribution function along these cracks directly, eliminating need for any indirect integral method. The method does not require meshing and hence idealisation of the shapes of the cracks, thereby improving accuracy and reducing pre- and post processing efforts. Interaction between the internal crack and the surface crack is examined in detail through several examples.