This paper describes a new solution technique for the equilibrium traffic assignment problem. After existing methods of solution are reviewed and difficulties that have been experienced with current techniques are discussed, a mathematical programming model for the equilibrium traffic assignment problem is presented. The solution technique for this programming model is one that has been proved to converge every time and that rapidly closes in on the equilibrium flows without excessive computational requirements. It is noted that the computational requirement of the proposed approach is very similar to those of currently used solution methods, which clearly indicates the feasibility of using the proposed approach to find the equilibrium flows on networks with hundreds of nodes. Numerical results for the proposed solution technique on a test network having 76 arcs and 24 nodes are given. A computing time (central processing unit) of 6 seconds on the CDC 6400 computer is reported for accurately computing the equilibrium flows on the test network.