In this paper structural response to dynamic loading, which is expressed in terms of displacements of the structure, is studied. A two-way asymmetrical multistory building model is subjected to bi-directional harmonic and earthquake loadings. The time histories of the vertically and horizontal displacements and rotation of the roof are obtained using the scaled boundary finite-element method. The program Dynamic Soil-Structure Interaction Analysis which takes into account the soil-structure interaction effects is applied to study two-way asymmetrical buildings.These results are compared with those of symmetrical buildings. Key words: Dynamic soil structure interaction, scaled boundary finite-element method, displacements, time varying loading.