In this paper we consider the solution of a dynamic traffic network model with elastic demands formulated as a projected dynamical system. We propose a discrete-time algorithm, the Euler method, which resolves the problem at each iteration into subproblems in path flow variables, all of which can be solved simultaneously and in closed form. Convergence results are also presented. We then discuss the implementation of the algorithm in CM Fortran on the massively parallel architecture, the Thinking Machine’s CM-5. Finally, we present numerical results for the parallel implementation on the CM-5 and for a serial implementation of the algorithm in Fortran on the IBM SP2 for several traffic network examples.