(Received 16 June 1993; in revised form 5 July 1993)
The membrane system with a non-cylindrical pore has been considered. The internal surface of a pore has been approximated by a hyperboloid of rotation. A simple analytical expression for the steady state electric potential distribution has been found. It has been shown that the obtained expression appeared to be exact for two limiting cases of cylindrical pores of a small radius and non-cylindrical pores of a large radius. This gives an opportunity to describe pore evolution when both its size and its shape are being changed. An example of pore evolution in a bilayer lipid membrane is considered, and the different variants of evolution are discussed.