A new semi-analytical boundary element method is proposed for determining the wheel-rail contact zone and the normal stress distribution within it. The potential contact area is discretised using strip elements, employing an iterative algorithm to satisfy the contact constraints. At each iteration, the length of the contact strips is updated using an analytical expression based on Hertz's theory. This simplified formulation provides good approximation of the pressure distribution and consequently the contact area in non-elliptic cases. The reduction in the number of system unknowns by using a semi-analytical methodology also enables fast computation speeds, an indispensable requirement in railway dynamics.