We describe a new suite of computational benchmarks that models applications featuring multiple levels of parallelism. Such parallelism is often available in realistic .ow computations on systems of meshes, but had not previously been captured in benchmarks. The new suite, named NPB (NAS Parallel Benchmarks) Multi-Zone, is extended from the NPB suite, and involves solving the application benchmarks LU, BT and SP on collections of loosely coupled discretization meshes. The solutions on the meshes are updated independently, but after each time step they exchange boundary value information. This strategy provides relatively easily exploitable coarse-grain parallelism between meshes. Three reference implementations are available: one serial, one hybrid using the Message Passing Interface (MPI) and OpenMP, and another hybrid using a shared memory multi-level programming model (SMP+OpenMP). We examine the effectiveness of hybrid parallelization paradigms in these implementations on three different parallel computers. We also use an empirical formula to investigate the performance characteristics of the hybrid parallel codes.