We analyze the transmission of highly charged ions (HCI) through microcapillaries. The interaction of an HCI with the interval surface of the capillary is treated within the framework of linear response. In the limiting case of an ideal conducting cylindrical surface, the interaction reduces to a classical image potential. For Neq+ projectiles transmitting through a Ni capillary calculations for the impact parameter distribution and angular distribution of hollow atoms are presented. We find the fraction of transmitted projectiles which are partially neutralized in good agreement with recent experiments.