Tree structures are used extensively in domains such as computational biology, pattern recognition, computer networks, and so on. In this paper, we present an indexing technique for free trees and apply this indexing technique to the problem of mining frequent subtrees. We first define a novel representation, the canonical form, for rooted trees and extend the definition to free trees. We also introduce another concept, the canonical string, as a simpler representation for free trees in their canonical forms. We then apply our tree indexing technique to the frequent subtree mining problem and present FreeTreeMiner, a computationally efficient algorithm that discovers all frequently occurring subtrees in a database of free trees. We study the performance and the scalability of our algorithms through extensive experiments based on both synthetic data and datasets from two real applications: a dataset of chemical compounds and a dataset of Internet multicast trees.