In this investigation, a numerical procedure for wheel/rail contact problems in the analysis of curve negotiation of railroad vehicles is developed using constraint/elastic contact approach. In particular, this work focuses on the flange contact detection algorithm using the two-point look-up contact table and the switching algorithm from the elastic to constraint contact for the flange climb simulation. The two-point look-up contact table is used for the contact search of the second point of contact modeled using the elastic contact, while the constraint contact is used for the first point of contact on the wheel tread. Furthermore, in the flange climb simulation using the constraint contact formulation, loss of a tread contact modeled using the constraint contact occurs. Therefore, the elastic contact used for modeling the flange contact in the two-point contact state needs to be switched to the constraint contact as soon as loss of the tread contact occurs. For this reason, if the Lagrange multiplier associated with the contact constraint becomes greater than or equal to zero, the elastic contact used for the flange is switched to the constraint contact. The computational algorithm for the proposed switching algorithm is also presented. Several numerical examples are presented in order to demonstrate the use of the numerical procedure developed in this investigation for modeling the two-point tread/flange contact as well as the flange climb behavior. Numerical results are in good agreement with those of the existing fully elastic contact formulation. Furthermore, it is shown that significant reduction in CPU time is achieved using the numerical procedure developed in this investigation.