Summary: We present a constructive design of a new class of cascaded network structures for broadcast applications called ring sandwich networks. These ring sandwich networks are rearrangeable in the sense that a request for a connection between a sender and a receiver can sometimes be realized only by first rearranging other existing connection paths through the network. We present analytical results which permit the average rearrangeability of ring sandwich networks to be evaluated on the basis of fundamental structural parameters associated with the ring sandwich design so that the trade-off between the network rearrangeability and the network cost can be determined. It will be shown that the average number of rearrangements to satisfy a broadcast connection request relative to the subnetwork of the cascaded ring sandwich structure providing fanout can be reduced to \(O(1)\); this is in contrast to \(O(N)\) for other existing cascaded designs. We will give detailed connecting algorithms that can be used to satisfy connection requests. We will also support our analytically derived results with corroborating simulation data. This work provides an analytical framework for a class of low-cost broadcast networks currently being employed by government and industry in both broadcasting and conferencing applications wherein only a limited degree of rearrangements can be tolerated.