A system of two conductors connected by spacers in the form of rigid rods is considered. The conductors are affected by the wind flow so that one conductor is in the aerodynamic (satellite) wake of the other, which leads to the emergence of a self-oscillating process. The wake interaction between conductors is modeled with a modified Simpson theory using Blevins and Prices empirical data. Differential equations are derived based on the principle of possible displacements in generalized coordinates, taking into account the nonlinearities of elastic and inertial forces, as well as aerodynamic forces in the wake. For discretization by spatial coordinates, the finite element method is used with the choice of linear and trigonometric shape functions as the basis. The tension force and the longitudinal deformation of the conductor are considered constant values within the element. The dependence of deformation on transverse displacements is determined by a quadratic approximation. To obtain final expressions for aerodynamic forces, polynomial approximations of known experimental data are used, as well as linearization of expressions for these forces written in local (elemental) coordinates.