Flaring and warping of the disk of the Milky Way have been inferred from observations of atomic hydrogen but stars associated with flaring have not hitherto been reported. In the area beyond the Galactic centre the stars are largely hidden from view by dust, and the kinematic distances of the gas cannot be estimated. Thirty-two possible Cepheid stars (young pulsating variable stars) in the direction of the Galactic bulge were recently identified. With their well-calibrated period-luminosity relationships, Cepheid stars are useful distance indicators. When observations of these stars are made in two colours, so that their distance and reddening can be determined simultaneously, the problems of dust obscuration are minimized. Here we report that five of the candidates are classical Cepheid stars. These five stars are distributed from approximately one to two kiloparsecs above and below the plane of the Galaxy, at radial distances of about 13 to 22 kiloparsecs from the centre. The presence of these relatively young (less than 130 million years old) stars so far from the Galactic plane is puzzling, unless they are in the flared outer disk. If so, they may be associated with the outer molecular arm.