When a fluid is pumped into a cavity in a confined elastic layer, at a critical pressure,
destabilizing fingers of fluid invade the elastic solid along its meniscus (Saintyves B. et al., Phys.
Rev. Lett., 111 (2013) 047801). These fingers occur without fracture or loss of adhesion and
are reversible, disappearing when the pressure is decreased. We develop an asymptotic theory
of pressurized highly elastic layers trapped between rigid bodies in both rectilinear and circular
geometries, with predictions for the critical fluid pressure for fingering, and the finger wavelength.
Our results are in good agreement with recent experimental observations of this elastic interfacial instability in a radial geometry. Our theory also shows that, perhaps surprisingly, this
lateral-pressure–driven instability is analogous to a transverse-displacement–driven instability of
the elastic layer. We verify these predictions by using non-linear finite-element simulations on the
two systems which show that in both cases the fingering transition is first order (sudden) and
hence has a region of bistability.