A tape cassette includes a pair of tape hubs to which the opposite ends of a magnetic tape are secured. The tape running is conventional in that the magnetic tape wound on one of the tape hubs is taken upon on the other tape hub. The pair of apertures for receiving the tape hubs are formed as elongated elliptical slots. When the tape cassette is loaded in a tape recorder and a tape winding operation has proceeded until its one end is reached, the tension applied to the tape by the winding effort of the take-up hub shaft causes a displacement of the tape hub within its associated aperture, thereby permitting the end of tape to be detected for automatically stopping the tape recorder by either electrically or mechanically rendering the operating mechanism of the recorder inoperative. Alternatively, the end of tape detection may be utilized to activate an end of tape alarm.