There is a growing number of web services available on the Internet, providing a wide range of functionalities. This diversity introduces a variety of new challenges in the field of software engineering — service discovery, integration, and composition, all of which require, to some extent, “service matching”. Web-service matching (or alignment) is the task of mapping the functionalities of two web services, assuming that these functionalities overlap somewhat. In this paper we propose a novel graph-theoretic approach, called Semantic Flow Matching (SFM), for matching REST web services, specified in WADL (Web Application Description Language). The method builds a heterogeneous network of WADL elements and semantically related terms, and uses this network to match similar functionalities of different web services. The method is implemented in a prototype tool that consists of two modules: a converter and a mapper; where the converter wraps the REST web services in WADL format and the mapper module matches web services based on their semantics extracted from the WADL interface build by the converter. We demonstrate the potential of the approach with a small case study.