  The aim of this paper is to study the Wold-type decomposition in the class of
$m$-isometries. One of our main results establishes an equivalent condition for
an analytic $m$-isometry to admit the Wold-type decomposition for $m\ge2$. In
particular, we introduce the $k$-kernel condition which we use to characterize
analytic $m$-isometric operators which are unitarily equivalent to unilateral
operator valued weighted shifts for $m\ge2$. As a result, we also show that
$m$-isometric composition operators on directed graphs with one circuit
containing only one element are not unitarily equivalent to unilateral weighted
shifts. We also provide a characterization of $m$-isometric unilateral operator
valued weighted shifts with positive and commuting weights.
