A theoretical investigation has been made of periodic and non-periodic combination resonances of the system of rods under vertical and horizontal kinematic excitations. The elements of the system are connected with articulated points. The coupling of the elements of the system through internal longitudinal forces, which are transverse forces at the ends of neighboring rods, are taken into account. The equations of motion are obtained from the Lagrange equations. The mathematical analysis of the equations of motion is accomplished by using Tondl’s technique. The steady state solutions and their stability are determined. Resonance curves for the stationary states have been determined numerically.