  A mixed finite element method combining an iso-parametric $Q_2$-$P_1$ element
and an iso-parametric $P_2^+$-$P_1$ element is developed for the computation of
multiple cavities in incompressible nonlinear elasticity. The method is
analytically proved to be locking-free and convergent, and it is also shown to
be numerically accurate and efficient by numerical experiments. Furthermore,
the newly developed accurate method enables us to find an interesting new
bifurcation phenomenon in multi-cavity growth.
