The present invention relates to a bearing system of a printing press and the printing press thereof. The bearing system is used for supporting a free end of a cylinder or a roller which is suspended in middle air and supported at one end of a flexographic printing press and is composed as a shaft journal, wherein, the baring system comprises at least one first housing which can move transversely with a longitudinal axis of the cylinder or the roller, a second housing which can move parallelly with the longitudinal axis of the cylinder or the roller in the first housing, and a rolling bearing. The second housing is basically provided with an outer circumferential surface which is arranged conically on the whole axial extension. The inclination angle (alpha) of the outer circumferential surface relatively to the longitudinal axis of the cylinder or the roller is smaller than or equal with 10 DEG, and is preferably smaller than or equal with 5 DEG. Furthermore the first housing is provided with an inner circumferential area which is composed correspondingly with the outer circumferential surface of the second housing that is arranged conically and is also arranged conically for forming an axial stop catch. Besides, the invention relates to the printing press with the bearing system, and particularly to the flexographic printing press.