Summary: Our work is motivated by the problem of managing data on storage devices, typically a set of disks. Such high-demand storage servers are used as Web servers or as multimedia servers for handling high demand for data. As the system is running, it needs to dynamically respond to changes in demand for different data items. In this work we study the data migration problem, which arises when we need to quickly change one storage configuration into another. We show that this problem is NP-hard. In addition, we develop polynomial-time approximation algorithms for this problem and prove a worst-case bound of 9.5 on the approximation factor achieved by our algorithm.