We develop and illustrate a numerical model for the evolution of a channel during and after removal of a dam. The most important new feature of the model is that it captures a phenomenon we have observed in experiments on dam removal: "erosional narrowing", a narrowing of the channel due to preferential erosion along the channel centerline and consequent flow restriction and spatial acceleration. The narrowing tendency is counterbalanced by the well known tendency of the channel to widen due to bank erosion. The interplay of these two effects can lead, among other things, to upstream propagation of waves of incision and sedimentation. The onset of narrowing is sensitive to the rate of fall of base level, controlled in the dam-removal case by the rate of draining of the reservoir. Ultimately, bank erosion and concomitant sedimetation in the channel center win out, leading to creation of a new channel profile with a lower streamwise slope.