In this paper, we present generalized and flexible problem formulations for safe and optimal evacuation routing with contraflow in transportation network. Avoiding the time-dependent formulation as seen in existing problem formulation, a more concise description of the evacuation routing is allowed. By considering the safe following distance and the travel speed as variables, a more flexible evacuation solution can be obtained. We present two problems in evacuation routing: to minimize the evacuation time and to determine contraflow for optimal evacuation and their mathematical formulations. We also show how the existing solutions can be used as the starting point of solving the new problems. We also briefly discuss one possible application of the proposed problems/solutions into another similar problem of mass transportation routing from an event parking.