We present a hybrid method for software model checking that combines explicit-state and symbolic techniques. Our method traverses the control flow graph of the program explicitly, and encodes the data values in a CNF formula, which we solve using a SAT solver. In order to avoid traversing control flow paths that do not correspond to a valid execution of the program we introduce the idea of a representative of a control path. We present favorable experimental results, which show that our method scales well both with regards to the non-deterministic data and the number of threads.