A novel method to shape the intensity distribution within an unstable laser cavity is demonstrated. This method is characterized by inscribing a tailored gain profile generated by a spatially tophat-shaped longitudinal pump beam into the gain medium. The mode shaping mechanism is still effective with zero output coupling. Therefore, this method enables to operate unstable laser cavities in cavity dump mode or as a regenerative amplifier. The theoretical background is described by means of geometrical optics, and operation of a prototype setup using cryogenically cooled Yb:YAG is demonstrated. The system produces 13ns pulses with 285 mJ at a repetition rate of 10 Hz, with an extraction efficiency of 35 %. Successful cavity dump operation is demonstrated with 110 mJ output energy.