Current design practices for the multistoried buildings ignore the presence of rotational components in the earthquake ground motion, though no substantial research has, so far, been done to validate this. An existing lack of recorded accelerograms for these rotational components has largely been responsible for the absence of significant efforts in this direction. Some of the recent developments in the generation of synthetic accelerograms have made it possible now to seriously consider this aspect in the seismic design of multistoried buildings.; A probabilistic approach based on the response spectrum superposition technique has been formulated for the building response to the earthquake excitation comprised of the rotational components along with the translational component. This approach is different from the other methods of spectrum superposition, as it can account for the interaction between various modes of vibration and further, the response peaks of all orders can be estimated with a reasonable degree of accuracy for the given level of confidence. The formulation has been presented first for the fixed base buildings and then, it has been suitably modified to account for the effects of soil-structure interaction.; Through several example buildings and different earthquakes and sites, it has been shown that there are certain situations in which, neglecting the rocking component may lead to unsafe designs. Effects of the torsional component on the. overall building response, on the other hand, have been found to be small.