The Resource Description Framework (RDF) has been ac- cepted as a standard for semantic representation of re- sources. Efficient methods and tools are needed to solve problems emerging from RDF based systems, for exam- ple, checking equality of two RDF graphs and retrieving subgraphs from another RDF graph. This paper proposes a method that encodes these problems into satisfiability (SAT) instances and solves them by employing efficient SAT solvers. A prototype tool is implemented and preliminary experimental results are given.