A device for irradiating tissue encompassing at least one electron source for generating an electron beam, numerous radiation heads that are firmly and annularly arranged in a supporting frame around an isocenter of the device and emit radiation towards the isocenter, and one beam guidance system to guide the electron beam in the housing towards the radiation heads. The beam guidance system has been built as a polygon, especially as a pentagon arranged like a ring around the isocenter, in which case media for deflecting the electron beam have been placed at every corner point of the polygon.