In the presented approach the simplified model of the guyed tower with a single guy line treated as a small-sag cable under stochastic seismic excitation is developed by using the Ritz method. Even if the source of the long-period ground motion occurs in greater distance from the structure it can results in its significant base displacements in the resonance region. That leads to the sway of the structure and its elastic bending deformation. Therefore, the considered guy line is excited by two sources: first one is the base motion at support point and second one is the horizontal vibrations of the tower at point where the cable is attached to the structure. The earthquake ground motions is modelled by using the Gaussian white noise process. The non-linear system of differential equations of motion is obtained by using the Ritz method and Lagrange’s equations. Finally, the longitudinal cable vibrations are coupled with the lateral ones. The equivalent linearization technique is used to determine the approximate mean values and the variances of particular random state variables. The condition of the minimization of the mean square error between the original non-linear system and the linear one is used to find the coefficients of the equivalent system. The obtained approximate analytical results are verified by the numerical Monte Carlo Simulation.