A description is given of a method and an arrangement for producing a laser beam with a linear beam cross section, which has a long and a short cross-sectional beam axis and has an extent in the long axis of at least 200 mm and an extent in the short axis of at most 800 [mu]m, wherein the laser beam emerging from a laser beam source is homogenized separately with respect to the long axis and the short axis, in that the laser beam is homogenized both in relation to the long axis and in relation to the short axis while respectively producing a focal plane, into which there are focused in each case a multiplicity of partial beams which have been created by dividing up the beam cross section of the laser beam and which are subsequently brought together to form a laser beam homogenized in the beam cross section, and the laser beam undergoes telecentric imaging, at least with respect to the long axis, i.e. the laser beam homogenized with respect to the long axis is projected by means of a condensing optical system (LACL) in such a way as to produce a path of rays that can be assigned to the projected laser beam, comprising partial beams of parallel light oriented longitudinally in relation to the direction of propagation. The invention is characterised by the following method steps: projecting the beam cross section that is converging in a homogenizing manner in the short axis by means of a first condensing optical system (SACL1) to produce a homogeneous image field (HFSA1) and producing a first pupil (P1) by means of a first field-lens optical system (SAFL1), into which the focal plane, in which the partial beams divided up with respect to the short axis are focused, is projected and projecting the homogeneous image field (HFSA1) by means of a second condensing optical system (SACL2) in a second image field (HSFA2) as well as projecting the first pupil (P1) by means of a second field-lens optical system (SAFL2) in a second pupil (P2).