Existing Searchable Encryption (SE) solutions are able to handle simple Boolean search queries, such as single or multi-keyword queries, but cannot handle substring search queries over encrypted data that also involve identifying the position of the substring within the document. These types of queries are relevant in areas such as searching DNA data. In this paper, we propose a tree-based Substring Position Searchable Symmetric Encryption (SSP-SSE) to overcome the existing gap. Our solution efficiently finds occurrences of a given substring over encrypted cloud data. Specifically, our construction uses the position heap tree data structure and achieves asymptotic efficiency comparable to that of an unencrypted position heap tree. Our encryption takes O(kn) time, and the resulting ciphertext is of size O(kn), where k is a security parameter and n is the size of stored data. The search takes O(m 2 + occ) time and three rounds of communication, where m is the length of the queried substring and occ is the number of occurrences of the substring in the document collection. We prove that the proposed scheme is secure against chosen-query attacks that involve an adaptive adversary. Finally, we extend SSP-SSE to the multi-user setting where an arbitrary group of cloud users can submit substring queries to search the encrypted data.