A processor array with spanning buses (PASB) is a well-known, versatile parallel architecture. A PASB is obtained from a two-dimensional mesh by replacing each linear connection with a bus. In this paper, we show how to optimally embed multiple copies of a graph into a PASB by a labeling strategy. Our embeddings simultaneously achieve an optimal expansion, congestion, and alignment cost. First, we propose a labeling scheme for anN-node graphG, possibly disconnected, such that this labeling makes it possible to optimally embed multiple copies ofGinto anN'xN' PASB whereN' is divisible byN. Second, we show that many important classes of graphs admit this labeling: for example, tree, cycle, mesh of trees, and product graphs such as mesh, torus, or hypercube. Finally, we show how to optimally embed multiple copies of a graph into a multidimensional and possibly nonsquare PASB.