The shape and stability of a drop with a sharp contact line are analyzed. The disjoining pressure is included. The choice made for the latter is special in that it admits a sharp contact angle as appropriate in this case. The stability analysis is considered for two scenarios, one where the contact line cannot be moved which mode turns out to be stable to small perturbations, and the other where it can be moved but the contact angle is fixed at the equilibrium value. This second case turns out to be unstable to small perturbations due to the curvature effect of the drop.