  Random union sets $Z$ associated with stationary Poisson processes of
$k$-cylinders in $\mathbb{R}^d$ are considered. Under general conditions on the
typical cylinder base a concentration inequality for the volume of $Z$
restricted to a compact window is derived. Assuming convexity of the typical
cylinder base and isotropy of $Z$ a concentration inequality for intrinsic
volumes of arbitrary order is established. A number of special cases are
discussed, for example the case when the cylinder bases arise from a random
rotation of a fixed convex body. Also the situation of expanding windows is
studied. Special attention is payed to the case $k=0$, which corresponds to the
classical Boolean model.
