In an ink supply method and system and an ink container where the ink is automatically supplied in the stencil printing, to permit suitable detection of empty of the ink container even if the kind of ink which has not been set is employed. A parameter representing an inkless time corresponding to the kind of ink (viscosity of ink) is stored in the storage means (8) provided on the ink container (10), the parameter is read out from the storage means (8) and the inkless time is set on the basis of the parameter, whereby it is recognized that the ink container is exhausted when the time for which the ink in the ink fountain (2) is not detected by an ink amount detecting means (40) becomes longer than the inkless time.