The performance of the Hopfield neural network with mean, field annealing for finding solutions to the shortest path problem in a communication network is investigated. The neural network uses mean j e l d annealing to eliminate the constraint terms in the energy function. Unlike other systems which use penalty constraint terms there is no need to tune constraint parameters (this tuning has been found to be difficult and problem specific). Also, we avoid the need to pre-determine the minimum number of hops corresponding to the optimal route. We have very encouraging simulation results for the nine node grid network and fourteen node NFSNET-backbone network but have found that the neural network has difficulty finding valid routes when many hops are required to get from the source to destination.