This paper describes some explicit constructions for reconfigurable array architectures. Given a working architecture (application graph), we add redundant hardware to increase reliability. The degree of reconfigurability, D R, of a redundant graph is a measure of the cost of reconfiguration after failures. When D^R is independent of the size of the application graph, we say the graph is finitely reconfigurable, F R. We present a class of simple layered graphs with a logarithmic number of redundant edges, which can maintain both finite reconfigurability and a fixed level of reliability for a wide class of application graphs. By sacrificing finite reconfigurability, we show that by using expanders we can construct highly reliable structures with the asymptotically optimal number of edges for one-dimensional and tree-like array architectures.