Abstract: The invention is directed to an arrangement for checking the tightness of a vessel such as a tank system of a motor vehicle. The vessel can have a possible leak and this can be viewed as a first flow resistor. The arrangement includes a pressure source for generating a pressure change in the vessel and a pressure divider system is connected between the pressure source and the vessel which is subjected to the pressure change. The pressure divider system is defined by and includes the first flow resistor and a reference branch having a predetermined second flow resistor. A pressure sensor measures the pressure relationships in the pressure divider system. The invention provides a reliable statement as to a possible leak in the tank system of a motor vehicle while providing a simple and therefore cost effective manufacture. The pressure source used to check the tightness can be utilized for other tasks required in a motor vehicle. The invention also relates to a method for checking the tightness of the vessel.