The emergence of cloud computing brought the opportunity to use large-scale computational infrastructures for a broad spectrum of applications and users. As the cloud paradigm gets attractive for the "elasticity" in resource usage and associated costs (the users only pay for resources actualy used), cloud applications still suffer from the high latencies and low performance of cloud storage services. Enabling high- throughput massive data processing on cloud data becomes a critical issue, as it impacts the overall application performance. In this paper we address the above challenge at the level of the cloud storage. We introduce a concurrency-optimized data storage system which federates the virtual disks associated to VMs. We demonstrate the performance of our solution for efficient data-intensive processing on commercial clouds by build- ing an optimized prototype MapReduce framework for Azure that leverages the benefits of our storage solution. We perform extensive microbenchmarks as well as experiments with real- world applications: they demonstrate that our solution brings substantial benefits to data intensive applications compared to approaches relying on state-of-the-art cloud object storage