The viscous flow inside an elliptic moving belt is studied using Newton's method on a Hermite collocation approximation. The streamlines and especially the vorticity distribution are found for Reynolds number up to 1000 and aspect ratio up to five. For low Reynolds numbers vorticity diffuses from regions of high curvature. For high Reynolds numbers there exists a closed boundary layer and a core of constant vorticity. The core vorticity compares well with the estimation from the mean square law
