Array redistribution is used in languages such as High Performance Fortran to allow programmers to dynamically change the distribution of arrays across processors. Distributed-memory implementations of several scientific applications require array redistribution. In this paper, efficient methods for performing array redistribution are presented. Precise closed forms for determining the processors involved in the communication and the data elements to be communicated are developed for two special cases of array redistribution involving block-cyclically distributed arrays. The general array redistribution problem involving block-cyclically distributed arrays can be expressed in terms of these special cases. Using the closed forms, a cost model for estimating the communication overhead for array redistribution is developed. A multi-phase approach for reducing the communication cost of array redistribution is presented. Experimental results on the Cray T3D to evaluate the multi-phase approach are provided.