Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: ${ullet}$ X is a divergence-free vector field satisfying the shadowing property. ${ullet}$ X is a divergence-free vector field satisfying the Lipschitz shadowing property. ${ullet}$ X is an expansive divergence-free vector field. ${ullet}$ X has no singularities and is Anosov.