<p>Printing on a cylindrical or conical surface of a container is carried out by a method and apparatus wherein the container is supported against rotation about a support axis. A squeegee is positioned at one side of a decorating screen to establish line contact between the opposite side of the screen and the surface of a container. The decorating screen is rolled along a tangential path about the surface of the container and concurrently the squeegee is moved along an orbital path about the support axis to force printing medium through the screen onto the surface of the container at the line of contact therewith.</p>