  A $k$-stack layout (also called a $k$-page book embedding) of a graph
consists of a total order of the vertices, and a partition of the edges into
$k$ sets of non-crossing edges with respect to the vertex order. The stack
number (book thickness, page number) of a graph is the minimum $k$ such that it
admits a $k$-stack layout. A $k$-queue layout is defined similarly, except that
no two edges in a single set may be nested.
  It was recently proved that graphs of various non-minor-closed classes are
subgraphs of the strong product of a path and a graph with bounded treewidth.
Motivated by this decomposition result, we explore stack layouts of graph
products. We show that the stack number is bounded for the strong product of a
path and (i) a graph of bounded pathwidth or (ii) a bipartite graph of bounded
treewidth and bounded degree. The results are obtained via a novel concept of
simultaneous stack-queue layouts, which may be of independent interest.
