The essential characteristics of an effective base isolation system are isolation, energy dissipation, and restoring mechanism. Some friction type base isolation systems proposed earlier have been found to be very effective in reducing the structural response and incorporate simple restoring mechanisms through gravity. However these isolators are effective only under certain excitation and structural characteristics. To overcome these limitations the authors have recently developed a new isolation system called the variable frequency pendulum isolator (VFPI) that has been found to be very effective under a variety of structure and excitation characteristics. In this paper, the mathematical formulation for the three dimensional behavior of an asymmetric structure isolated by a sliding type isolator, with particular reference to VFPI has been presented. The behavior of torsionally coupled structure isolated by VFPI has been examined. The factors affecting the torsional coupling of isolated structure have been identified. The behavior of structure isolated by VFPI has been compared with the structure isolated by other type of friction isolators such as friction pendulum system and pure-friction system.