  We investigate the cosmic ray driven dynamo in the interstellar medium of
irregular galaxy. The observations (Chyzy et al. 2000, 2003) show that the
magnetic field in irregular galaxies is present and its value reaches the same
level as in spiral galaxies. However the conditions in the medium of irregular
galaxy are very unfavorable for amplification the magnetic field due to slow
rotation and low shearing rate.
  In this work we present numerical model of the interstellar medium in
irregular galaxies. The model includes magnetohydrodynamical dynamo driven by
cosmic rays in the interstellar medium provided by random supernova explosions.
We describe models characterized by different shear and rotation. We find that
even slow galactic rotation with low shearing rate gives amplification of the
magnetic field. Simulations have shown that high amount of the magnetic energy
flow out off the simulation region becoming an efficient source of
intergalactic magnetic fields.
