Method and device for printing a web or a rectangular piece of material

In the process of printing a design on material using a rotary thin-walled cylindrical screen stencil having a squeegee therein wherein the design to be printed has a repeat length greater than the circumference of the stencil, the steps of forming on the screen surface of the stencil an impermeable area extending along a portion of the circumference of the stencil and the remaining portion of the stencil defining a screened area, conveying the material to be printed past the stencil, and vertically moving the squeegee during rotation of the stencil during the time interval that the impermeable area is contiguous with the material to be printed so that fading out and fading in of color during lifting and lowering of the squeegee is prevented, the stencil selectively does not print the material when the squeegee is out of contact with the screen surface and when the impermeable area is contiguous with the material and the stencil prints only when its squeegee is lowered and the screened area passes in contact with the material whereby a design having a repeat length greater than the circumference of the stencil can be printed.