For conformal contact situations, some of the assumptions employed in classical contact theories, such as the flatness of the contact area, lose their validity. Existing conformal contact models are challenged by either accuracy or computational efficiency. With the aim of achieving a balanced trade-off between these contrasting requirements, this paper proposes a new simplified method to solve conformal rolling contact problems, which is based on fast non-Hertzian contact model INFCON and FaStrip. Numerical experiments are performed for two typical wheel/rail conformal contact scenarios to assess the performance of the proposed method, taking as the reference the CONTACT method for conformal contacts. The comparative analyses show that the proposed method is in good agreement with the reference method in terms of the determination of the contact stresses, total forces, and the prediction of wear, whereas the traditional half-space approach fails to capture the main features of the conformal contacts. In addition, the high computational efficiency of the proposed method shows the potential for application in vehicle dynamic simulation and damage analysis.