The object of this report is to evaluate the possibility of applying polyhedral techniques to the parallel language OpenStream, which is developed by INRIA Parkas. When applicable, these techniques are invaluable for compile-time debugging and for improving the target code for a better adaptation to the target architecture. OpenStream is a two-level language, in which a sequential control code directs the initialization of parallel task instances that communicate through \emph{streams}. OpenStream programs are deterministic by construction, but may have deadlocks. If the control code is polyhedral, one may statically compute, for each task instance, its read and write indices for each stream. These indices may be polynomials of arbitrary degree. When linear, the full power of the polyhedral model may be brought to bear for dependence and dataflow analysis, scheduling and deadlock detection, and program transformations. In the general case, one can think of two approaches: the first one consists in over-approximating dependences until problems become linear. In the second approach, one first leverage modern developments in SMT solvers, which allow them to solve polynomial problems, albeit with no guarantee of success. Furthermore, the task index functions have special properties that may be used to construct original analysis algorithms. Three preliminary results in this direction are 1) the proof that deadlock detection is undecidable in general, 2) a characterization of deadlocks in terms of dependence graphs, which implies that streams can be safely bounded as soon as a schedule exists with such sizes, and 3) a preliminary analysis of some solvable cases.