When a dynamic load passes a control volume of material as a shock wave, passing this wave through the control volume could cause different phases such as elastic and plastic. From the microscopic view, during phase change, material flow would be taken in control volume which includes mass, heat, energy, and momentum transport. Phase change in material causes a material discontinuity in the control volume. During the phase change process, mass, heat, energy, momentum transport and etc will occur and the equations governing these phenomena are called transport equations. In this article, for the first time, the governing equations of elastoplastic behavior of beam under dynamic load are extracted by using mass, energy and momentum transport equations. Using transport equations with non-physical variables in integral form will cause in employing discontinuity conditions in governing equations and eliminates the discontinuity condition. These equations are also used in continuously modeling of beam elastoplastic behavior under dynamic loading and a continuous model is presented. Finite element method is used to solve the transport equation with non-physical variable. Finally, the time history of stress, strain and velocity wave propagation along beam are presented in elastic and elastoplastic phases