This study aims to evaluate the torsional effects and soil-structure interaction simultaneously under near-fault pulse-like earthquakes in a probabilistic framework. Incremental dynamic analysis and fragility curves are employed for this goal. An eight-story R/C dual lateral load-resistant building consisting of shear walls and moment resisting frames is used. The median incremental dynamic analysis curves reported the maximum capacity for the symmetric structure in each foundation conditions. In addition, the capacity of structure will be increased when more shear wave velocity is assumed. Therefore, from this view, neglecting the soil-structure interaction will not be in the safe side. Fragility curves (using intensity measure directly) show that for different cases (except for very low shear wave velocity), more value of eccentricity leads to more probability of collapse. Moreover, the fragility curves show that (for each eccentricity), soil-structure interaction effect is significant only for the flexible base structure with the very low shear wave velocity (100 m/s) and more eccentricity value leads to less soil-structure interaction effects. Results show that the significant eccentricity value may lead to reduce the soil-structure interaction effect in the shear-wall structures under the near-fault events.