  In the early 1990s, A. Bezdek and W. Kuperberg used a relatively simple
argument to show a surprising result: The maximum packing density of circular
cylinders of infinite length in $\mathbb{R}^3$ is exactly $\pi/\sqrt{12}$, the
planar packing density of the circle. This paper modifies their method to prove
a bound on the packing density of finite length circular cylinders. In fact,
the maximum packing density for unit radius cylinders of length $t$ in
$\mathbb{R}^3$ is bounded above by $\pi/\sqrt{12} + 10/t$.
