  Non-trivial $\phi ^{4}$-theory is studied in a renormalisation group
invariant approach inside a box consisting of rectangular plates and where the
scalar modes satisfy periodic boundary conditions at the plates. It is found
that the Casimir energy exponentially approaches the infinite volume limit, the
decay rate given by the scalar condensate. It therefore essentially differs
from the power law of a free theory. This might provide experimental access to
properties of the non-trivial vacuum. At small interplate distances the system
can no longer tolerate a scalar condensate, and a first order phase transition
to the perturbative phase occurs. The dependence of the vacuum energy density
and the scalar condensate on the box dimensions are presented.
