Motivated by emerging applications to the edge computing paradigm, we introduce a two-layer erasure-coded fault-tolerant distributed storage system offering atomic access for read and write operations. In edge computing, clients interact with an edge-layer of servers that is geographically near; the edge-layer in turn interacts with a back-end layer of servers. The edge-layer provides low latency access and temporary storage for client operations, and uses the back-end layer for persistent storage. Our algorithm, termed Layered Data Storage (LDS) algorithm, offers several features suitable for edge-computing systems, works under asynchronous message-passing environments, supports multiple readers and writers, and can tolerate f 1 < n 1 /2 and f 2 < n 2 /3 crash failures in the two layers having n 1 and n 2 servers, respectively. We use a class of erasure codes known as regenerating codes for storage of data in the back-end layer. The choice of regenerating codes, instead of popular choices like Reed-Solomon codes, not only optimizes the cost of back-end storage, but also helps in optimizing communication cost of read operations, when the value needs to be recreated all the way from the back-end. The two-layer architecture permits a modular implementation of atomicity and erasure-code protocols; the implementation of erasure-codes is mostly limited to interaction between the two layers. We prove liveness and atomicity of LDS, and also compute performance costs associated with read and write operations. In a system with n 1 = Θ(n 2 ), f 1 = Θ(n 1 ), f 2 = Θ(n 2 ), the write and read costs are respectively given by Θ(n 1 ) and Θ(1) + n 1 I(δ > 0). Here δ is a parameter closely related to the number of write operations that are concurrent with the read operation, and I(δ > 0) is 1 if δ > 0, and 0 if δ = 0. The cost of persistent storage in the back-end layer is Θ(1). The impact of temporary storage is minimally felt in a multi-object system running N independent instances of LDS, where only a small fraction of the objects undergo concurrent accesses at any point during the execution. For the multi-object system, we identify a condition on the rate of concurrent writes in the system such that the overall storage cost is dominated by that of persistent storage in the back-end layer, and is given by Θ(N ).