The suffix tree is a data structure for indexing strings. It is used in a variety of applications such as bioinformatics, time series analysis, clustering, and text editing and data compression. However, when the string and the resulting suffix tree are too large to t into the main memory, most existing construction algorithms become very inefficient. This paper presents a disk-based suffix tree construction method, called Elastic Range (ERa), which works efficiently with very long strings that are much larger than the available memory. ERa partitions the tree construction process horizontally and vertically and minimizes I/Os by dynamically adjusting the horizontal partitions independently for each vertical partition, based on the evolving shape of the tree and the available memory.