A stencil printing machine and a method carrying out a printing operation are disclosed wherein a print sheet is transferred through between an upstream printing drum and a press roller in a pressured state to transfer ink onto an upper surface of the print sheet and is then transferred through between a downstream printing drum and a press roller in a pressured state to transfer ink onto the other surface of the print sheet to perform a both sides printing operation. A printing-drum drive escape mechanism is located to shift the downstream printing drum to a drive escape position to interrupt rotation of the printing drum while retaining the press roller in a separated position away from the shifted printing drum in such a manner that the printing operation under such a condition in a one side printing mode is executed.