  Consider two parallel lines $\ell_1$ and $\ell_2$ in $\mathbb{R}^3$. A rail
arc is an embedding of an arc in $\mathbb{R}^3$ such that one endpoint is on
$\ell_1$, the other is on $\ell_2$, and its interior is disjoint from
$\ell_1\cup\ell_2$. Rail arcs are considered up to rail isotopies, ambient
isotopies of $\mathbb{R}^3$ with each self-homeomorphism mapping $\ell_1$ and
$\ell_2$ onto themselves. When the manifolds and maps are taken in the
piecewise linear category, these rail arcs are called stick rail arcs.
  The stick number of a rail arc class is the minimum number of sticks, line
segments in a p.l. arc, needed to create a representative. This paper will
calculate the stick numbers of rail arcs classes with a crossing number at most
2 and use a winding number invariant to calculate the stick numbers of
infinitely many rail arc classes.
  Each rail arc class has two canonically associated knot classes, its under
and over companions. This paper also introduces the rail stick number of knot
classes, the minimum number of sticks needed to create a rail arcs whose under
or over companion is the knot class. The rail stick number is calculated for
all knot classes with crossing number at most 9. The stick number of
multi-component rail arcs classes is considered as well as the lattice stick
number of rail arcs.
