Recent experiments by Prigent and Dauchot have shown that the remarkable spiral turbulence state of Taylor-Couette flow also occurs in plane Couette flow. In both cases, a pattern of alternating turbulent and laminar bands appears at a well-defined Reynolds number.The pattern is tilted with respect to the streamwise (or azimuthal) direction and its wavelength is much larger than the gap.The angle and wavelength depend systematically on Reynolds number. We have numerically simulated these turbulent-laminar patterns for plane Couette flow. In our computational approach, we replace the large lateral dimensions of the experiment by a narrow periodically repeating rectangle which is tilted with respect to the streamwise direction. In this way we determine which angles and lengths support turbulent bands.