  In this paper we study the stability of $n$-dimensional constant mean
curvature unduloids embedded in slabs in $\mathbb{R}^{n+1}$. We prove that
among the family of half period unduloids stability is determined by whether
the volume is increasing or decreasing along this family provided some
conditions on the volume function are met. We then use this theorem to prove
the existence of stable unduloids of dimension eight.
