We report observations of convective motion in a container filled with granular material when it is vibrated in the horizontal direction. We find that the roughness of the boundaries and the container dimensions play an important role in determining the shape and number of the convection cells. When the container bottom and lateral walls are rough, the system typically exhibits four counter-rotating rolls stacked in two pairs on top of each other; for very low filling height, it is possible to observe a single row of rolls arranged laterally along the bottom of the container. With smooth walls, on the other hand, we find that the system typically forms only a single pair of counter-rotating convection rolls that originate in the two upper corners of the vibrated material; when the filling height is increased to a level that depends on the container width, we observe a transition to the four-roll state. (c) 1999 American Institute of Physics.