  In this fluid dynamics video, we study a two-phase flow in an elastic
Hele-Shaw cell that involves two distinct fluid- and solid-based instabilities:
viscous fingering and sheet buckling. We show that the relative importance of
the two instabilities is controlled by a single non-dimensional parameter,
which provides a measure of the elasticity of the flexible wall. We employ
numerical simulations to show that for relatively stiff [soft] walls, the
system's behaviour is dominated by viscous fingering [sheet buckling]. Strong
interactions between the two instabilities arise in an intermediate regime and
lead to the development of extremely complex fingering and buckling patterns.
