In the electrostatic approximation, the problem on the propagation of an electric signal along a thin layer that models a cell membrane has been considered. On both sides of the membrane, volume conductors with different properties are present. Different types of boundary conditions have been investigated. In the cases of a cylindrical fiber and a plane layer, solutions have been found and compared with the relations used in the classical Hodgkin-Huxley cable theory of membrane potential propagation. Conditions under which the results obtained coincide with the conclusions of this theory have been formulated. It is shown that the results are in agreement with the cable theory only if the system is completely symmetric and the near-membrane layers are thin.