Decision making requires possibilities to influence the object. In urban traffic area it is crucial to influence traffic flows. However, first of all, decision maker needs comprehensive information about traffic flows. From a practical perspective, the most valuable is information about route flows, unlike information about link flows. In this paper, a route flow traffic assignment model in a linear network is studied. Linear road network (linear link performance function) gives a chance to reduce traffic assignment problem to a system of linear equations and conditions in the form of linear inequalities. The directed graph represents road network. Route flow traffic assignment problem is presented as a nonlinear constrained problem. The theorem about the reduction of a route flow traffic assignment problem in linear road network to the system of linear equations is proved. Implementation of developed approach to an example of the linear road network is disassembled in details.