This note presents an algorithm for the solution of the traffic assignment problem with elastic demands. The algorithm is based on the concept of "equilibration operator" introduced by Dafermos and Sparrow (1969) for the solution of the traffic assignment problem with fixed demands. Computational experience is provided for linear and nonlinear problems for both the algorithm proposed here and the Dafermos-Sparrow algorithm applied to the "excess-demand" reformulations of the problems.