Abstract In this paper are researched torsional fluctuations of structure located on the pendulum system of seismic isolation (SIS). Torsional oscillations are caused by the incongruence of the center of rigidity (CR) with the center of mass (CM) of the structure and influence of rotational ground motions. In the calculations given below is considered only the first reason. The lack of coincidence of CR and CM leads to an asynchronous motion of different pendulum devices and to their different longitudinal deformation. Thereby, the tension and compression forces of the devices are different. This leads to the torsion, rocking and vertical displacement of the seismically isolated structure. This paper investigates the influence of the above-mentioned effects.