The flame bending process can be most useful in the present effort to automate the plate bending process in shipyards. To achieve this goal, the complicated thermo-elastic-plastic behavior of the plate during the process must be understood. A review of the past analytical research efforts reveals that these attempts have been restricted to beam bending. Here a theory for the thermo-elastic-plastic plate bending is developed. Furthermore, using a boundary element method as a solution technique, the difference between the mechanics of beam bending versus plate bending is shown. Recommendations for future work are given.