  A regular $A_n$-crystal is an edge-colored directed graph, with $n$ colors,
related to an irreducible highest weight integrable module over
$U_q(sl_{n+1})$. Based on Stembridge's local axioms for regular simply-laced
crystals and a structural characterization of regular $A_2$-crystals in
\cite{DKK-07}, we present a new combinatorial construction, the so-called {\em
crossing model}, and prove that this model generates precisely the set of
regular $A_n$-crystals.
  Using the model, we obtain a series of results on the combinatorial structure
of such crystals and properties of their subcrystals.
