A non-stop rack device for temporary receipt of the flat elements in the form of sheets in a converting machine, the device comprising a plurality of parallel bars which are integral with a mobile support which can be displaced between a receipt position, in which the bars can support temporarily the flat elements which are being stacked, and a released position, in which the said bars are placed spaced from any stack of flat elements. Each non-stop bar is mounted so as to be mobile in transverse displacement relative to the mobile support, and the non-stop rack device also comprises a blocking arrangement, which can block the transverse mobility of each non-stop bar.