The seismic response history analysis of multi-storey asymmetric adjacent buildings with soil-structure interaction (SSI) during impact is investigated in this study. The coupled multi-degree of freedom modal differential equations of motion for the two way asymmetric shear buildings are derived and solved using a step by step solution by the fourth-order Runge-Kutta method with impact and without impact. The SSI forces are modelled in the form of the frequencyindependent soil springs and dashpots. A numerical example of two-way asymmetric four-storey adjacent buildings under the variation of the important SSI system parameters such as the large and small SSI effects is investigated under the excitation of the 1940 El Centro Earthquake. This study shows that the lateral torsion response of both buildings is affected when impact takes place with the adjacent buildings. The first three modal response histories of each building are significantly reduced due to the effect of the small SSI. Further, it is also observed that the roof twist of the lighter buildings is decreased for the large SSI effect compared to the small SSI effect. Finally, in increased eccentricities, the impact response of buildings is significantly severe.