If problems involving unstructured meshes are to be solved efficiently on distributed‐memory parallel computers, the meshes must be partitioned and distributed across processors in a way that balances the computational load and minimizes communication. The recursive spectral bisection method (RSB) has been shown to be very effective for such partitioning problems compared to alternative methods, but RSB in its simplest form is expensive. Here a multilevel version of RSB is introduced that attains about an order‐of‐magnitude improvement in run time on typical examples.