The object in an arrangement for pumping an anisotropic laser crystal is to reduce the influence of the destruction limit of the laser crystal on increased pump power density and, in this connection, to achieve improved beam quality and increased efficiency of a diode-pumped solid state laser. At the same time, the pump volume and cross-sectional area are to be kept as small as possible along a length of the crystal corresponding at least approximately to the absorption length. The arrangement operates with an asymmetric pump beam whose pump beam cross section has different dimensions perpendicular to one another and with a laser beam cross section which is adapted to this asymmetry. That axis of the crystallographic axes of the anisotropic laser crystal in whose direction the highest value of the crystal breaking limit exists is oriented along the greatest temperature gradient in the direction of the smaller dimension of the pump beam cross section.