We demonstrate results of design and optimization of high average output power picosecond laser operating at 1342 nm wavelength for selective material processing. This laser is comprised of mode locked master oscillator, regenerative amplifier and output pulse control module. Passively mode locked by means of semiconductor saturable absorber and pumped with 808 nm wavelength Nd:YVO4 master oscillator emits pulses of ~ 13 ps duration at repetition rate of 55 MHz with average output power of ~ 140 mW. The four-pass confocal delay line with image relay forms a longest part of the oscillator cavity in order to suppress thermo-mechanical misalignment. Optimization of the intracavity pulse fluence ensures significant lifetime improvement for the saturable absorber. This oscillator was used as the seeder for regenerative amplifier based on composite diffusion-bonded Nd:YVO4 rod pumped with 880 nm wavelength. When operating at 300 kHz repetition rate the laser delivers high quality output beam of M2 ~ 1.1 with average power in excess of 10 W at 1342 nm wavelength.