Abstract: Overflow cost means the cost that is delivered to users when the transportation load of a route exceeds the standard load of this route. When the load is lower than the standard, the costwill be given to users as an allowance. Through taking the overflowcost into consideration, the authors set up some restraint conditions, such as dynamical user optimum route choice condition and dynamical user optimum overflow cost,etc. Thismakes a basis forthe furtherresearchon founding a route choice variational inequalitymodel of dynamical transportation networks with overflow cost, and on its algorithm study.