A variety of wave patterns are found to form in a thin layer of sand inside a cylinder rotated about its horizontal axis of symmetry at constant angular velocity. In particular, we observe a spanwise instability characterized by serrated frontal shapes remarkably similar to those seen in Newtonian fluids. Within a certain parameter range, an accompanying spatial pattern forms on the rising side of the cylinder and travels along the cylinder span. The associated phase velocity is relatively constant, whereas the relevant wavelength increases quadratically with angular rotation speed. Standing waves appear at a critical rotation rate. Further, in some cases, a propagating cellular pattern forms on the surface of the medium. ©1998 American Institute of Physics.