We present in detail the algorithm of the electrostatic–quasi-stationary–electromagnetic/MHD approximations and equivalent external sources (EQUEMES method) to develop the quasi-stationary–electromagnetic models of seismo-ionospheric coupling. The penetration of the electromagnetic feld created by near-Earth alternative currents of ULF range was simulated by solving equations for the horizontal electric feld components Ex, Ey of the second order with respect to the vertical coordinate z. This system of two second-order equations is derived from the system of Maxwell equations. The penetration of rather strong horizontal electric feld [of order of (1–10) mV/m] to the ionospheric E and F layers has been modeled. The corresponding variations in the electron concentration in the E and lower F layers of the ionosphere reach a value of order of (1–10)%. Farther increase in these variations can be connected with the related synergetic processes. A possibility of the efective initiation of electron concentration perturbations in the unstable near-equatorial plasma in the F layer of the ionosphere by the packet of atmospheric gravity waves radiated by the near-ground source is illustrated. A good correspondence of the results obtained on the basis of this model to the data of satellite observations is shown.