The case when the potential distribution inside a corrosion cavity obeys Ohm's law is considered. Mathematically, the potential drop in the crevice is described by a Poisson-type equation with a non-linear source term. A simple method for finding all possible solutions in a one-dimensional approximation and for investigating their stability has been developed. We derive a simple relation for estimating the critical depth of the crevice, L-c (which is defined as the depth at which the active-passive transition just occurs within the crevice) as a function of the width of the crevice, w, electrolyte conductivity, K, metal potential, E-met, and a polarization curve. It is shown that L-c is proportional to root(wK) and is a linear function of E-met. Calculation of the corrosion damage (maximum depth of the penetration into the metal, W-max) as a function of time and position inside the crevice has been performed. It is shown that during the initial stages of crevice corrosion, when the one-dimensional approximation is valid, W-max is determined mainly by the polarization curve for the anodic dissolution of the metal. It is shown that, in the general case, it is impossible to neglect the potential drop in the external environment when quantitatively describing crevice corrosion. (C) 2012 Elsevier Ltd. All rights reserved.