This paper describes a simple and efficient procedure for the treatment of conformal contact conditions with special emphasis on railroad wheel/rail contacts. The general three-dimensional nonconformal contact conditions are briefly reviewed. These nonconformal contact conditions, which are widely used in many applications because of their generality, allow for predicting online one point of contact, provided that the two surfaces in contact satisfy certain geometric requirements. These nonconformal contact conditions fail when the solution is not unique as the result of using conformal surface profiles or surface flatness, situations often encountered in many applications including railroad wheel/rail contacts. In these cases, the Jacobian matrix obtained from the differentiation of the nonconformal contact conditions with respect to the surface parameters suffer from singularity that causes interruption of the computer simulations. The singularities and the fundamental issues that arise in the case of conformal contact are discussed, and a simple and computationally efficient procedure for avoiding such singularities in general multibody systems (MBS) algorithms is proposed. In order to demonstrate the use of the proposed procedure, the wheel climb of a wheelset as the result of an external lateral force is considered as an example. In this example, the wheel and rail profiles lead to conformal contact scenarios that could not be simulated using the nonconformal contact conditions.