  We consider the evolution of fronts by mean curvature in the presence of
obstacles. We construct a weak solution to the flow by means of a variational
method, corresponding to an implicit time-discretization scheme. Assuming the
regularity of the obstacles, in the two-dimensional case we show existence and
uniqueness of a regular solution before the onset of singularities. Finally, we
discuss an application of this result to the positive mean curvature flow.
